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------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD0QAAAAYAIQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAHAAAA/AIAAP///wAAAAQAAAAtAQMABAAA ACcB//8cAAAA+wLU/wAAAAAAAJABAAAAAABAAABBcmlhbAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAQAAAAtAQQABAAAAC4BGAAEAAAAAgEBAAUAAAAJAgAAAAIhAAAAMgo2AE8BEQAAAFJ1bGVz IG9mIFJhZGljYWxzACAAGAAKABkAFgANABgADQAMACAAGQAYAAoAFgAYAAoAFgAEAAAALgEAABwA AAD7AhAABwAAAAAAvAIAAAAAAQICIlN5c3RlbQAAAAAAABgAAAAsnhMAAgAAAOQEAAAAAAAABAAA AC0BBQAEAAAA8AEEAAMAAAAAAA== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0018.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0051.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0051_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhTwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAABM AAIAgAAAAAAAAAITjI95wO0PgZohMoozsvzpZX1BAQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0052.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0052_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAAAAIFjI+pywUAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0052_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAEAgAAAAAAAAAIHjI8Iy5t/CgA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0052_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAIAgAAAAAAAAAILjI8Iy5wPY2hUogIAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0052_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0053.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use th= ese rules to simplify root-expressions.
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0053_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAAAAIFjI+pywUAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0053_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAEAgAAAAAAAAAIHjI8Iy5t/CgA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0053_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAIAgAAAAAAAAAILjI8Iy5wPY2hUogIAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0053_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0054.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0054_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAAAAIFjI+pywUAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0054_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAEAgAAAAAAAAAIHjI8Iy5t/CgA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0054_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAIAgAAAAAAAAAILjI8Iy5wPY2hUogIAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0054_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0055.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0055_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0055_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAAAAIFjI+pywUAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0055_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAEAgAAAAAAAAAIHjI8Iy5t/CgA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0055_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAIAgAAAAAAAAAILjI8Iy5wPY2hUogIAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0055_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0056.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0056_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0056_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAo AAEAgAAAAAAAAAIHjI8Iy5sPCwA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0056_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAAAAIFjI+pywUAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0056_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAEAgAAAAAAAAAIHjI8Iy5t/CgA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0056_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAIAgAAAAAAAAAILjI8Iy5wPY2hUogIAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0056_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0057.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0057_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0057_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhVwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABV AAEAgAAAAAAAAAIMjI8Iy5sPm5y0AggLADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0057_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAAAAIFjI+pywUAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0057_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAEAgAAAAAAAAAIHjI8Iy5t/CgA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0057_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAIAgAAAAAAAAAILjI8Iy5wPY2hUogIAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0057_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3D
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAEAgAAAAAAAAAIEjI95BQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhVwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABV AAEAgAAAAAAAAAIMjI8Iy5sPm5y0AggLADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAIAgAAAAAAAAAIFjI+pywUAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAEAgAAAAAAAAAIHjI8Iy5t/CgA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhJwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAk AAIAgAAAAAAAAAILjI8Iy5wPY2hUogIAOw== ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0058_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0059.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
c. Öx2y
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
c. Öx2y =3DÖx2Öy
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
c. Öx2y =3DÖx2Öy =3D xÖy
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
d. Öx2y3
c. Öx2y =3DÖx2Öy =3D xÖy
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
d. Öx2y3 =3DÖx2y2Öy
c. Öx2y =3DÖx2Öy =3D xÖy
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
d. Öx2y3 =3DÖx2y2Öy =3D xyÖy
c. Öx2y =3DÖx2Öy =3D xÖy
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Example A.  Simplify
 
<= span style=3D'font-size:133%;color:#003300'>a.Ö8 =3D Ö4Ö2 =3D 2Ö2
Square Ru= le: Öx =3DÖx Öx<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'> =3D x if x > 0.
Multiplic= ation Rule: Öx<= span lang=3DEN-US style=3D'font-family:Arial;mso-bidi-font-family:Arial;mso-han= si-font-family: Arial;font-size:133%;mso-fareast-language:ZH-CN'>·y =3D Öx·&Ou= ml;y =
We use these rules to simplify root-expressions.  &= #13;
In particular, look for square factors of the radicand to pull out when simplifying square-root.
Rules of Radical= s
b. Ö72 =3DÖ36Ö2 =3D 6Ö2
d. Öx2y3 =3DÖx2y2Öy =3D xyÖy
c. Öx2y =3DÖx2Öy =3D xÖy
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
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A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0068.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0068_image146.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0069.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0069_image147.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0069_image148.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0069_image149.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAY AAEAgAAAAAAAAAIEjI+pVwA7 ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0070.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet)
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0070_image150.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0070_image151.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0070_image152.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABR AAEAgAAAAAAAAAIMjI+pBu0Po5xuWVQAADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0071.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet) = ;
        = ;  =3D 2Ö9Ö2
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0071_image153.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0071_image154.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0071_image155.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABR AAEAgAAAAAAAAAIMjI+pBu0Po5xuWVQAADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0071_image156.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAb AAEAgAAAAAAAAAIGjH+gu+gFADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0072.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet) = ;
        = ;  =3D 2Ö9Ö2 =3D 2*<= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >3*Ö2
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0072_image157.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0072_image158.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0072_image159.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABR AAEAgAAAAAAAAAIMjI+pBu0Po5xuWVQAADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0072_image160.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0072_image161.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAb AAEAgAAAAAAAAAIGjH+gu+gFADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0073.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet) = ;
        = ;  =3D 2Ö9Ö2 =3D 2*<= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >3*Ö2 =3D 6Ö2 (simplified)
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0073_image162.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0073_image163.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0073_image164.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABR AAEAgAAAAAAAAAIMjI+pBu0Po5xuWVQAADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0073_image165.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0073_image166.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0073_image167.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAb AAEAgAAAAAAAAAIGjH+gu+gFADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet) = ;
        = ;  =3D 2Ö9Ö2 =3D 2*<= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >3*Ö2 =3D 6Ö2 (simplified) <= /div>
b.Ö80x4y5
Rules of Radical= s
------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074_image168.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074_image169.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhDwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAQAP AAEAgAAAAAAAAAIDjI9ZADt= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074_image170.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAABR AAEAgAAAAAAAAAIMjI+pBu0Po5xuWVQAADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074_image171.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhMwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAx AAEAgAAAAAAAAAIGjI+py40FADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074_image172.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074_image173.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAJ AAEAgAAAAAAAAAIDjH8FADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0074_image174.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAb AAEAgAAAAAAAAAIGjH+gu+gFADs= ------=_NextPart_01C969FB.91DFA270 Content-Location: file:///C:/0EC311F3/2RulesofRadicals_files/slide0075.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Rules of Radicals
A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet) = ;
        = ;  =3D 2Ö9Ö2 =3D 2*<= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >3*Ö2 =3D 6Ö2 (simplified) <= /div>
b.Ö80x4y5 = =3D Ö16·5x4y4y
Rules of Radical= s
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A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet) = ;
        = ;  =3D 2Ö9Ö2 =3D 2*<= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >3*Ö2 =3D 6Ö2 (simplified) <= /div>
b.Ö80x4y5 = =3D Ö16·5x4y4y
        = ;      =3D 4x2y2Ö5y
Rules of Radical= s
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A radical expression is said to be simplifie= d if as muc= h as possible = is extracted out of the square-root.
Example B. Simplify.
 
a. Ö72 =3D Ö4 = Ö18 =3D 2Ö18 (not simplified yet) = ;
        = ;  =3D 2Ö9Ö2 =3D 2*<= span lang=3DEN-US style=3D'font-size:133%;color:red;mso-fareast-language:ZH-CN'= >3*Ö2 =3D 6Ö2 (simplified) <= /div>
b.Ö80x4y5 = =3D Ö16·5x4y4y
        = ;      =3D 4x2y2Ö5y
Rules of Radical= s
Division = Rule:
 y
x
Öy
Öx
Ö
=3D
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