document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=406070>Question 406070</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are the steps to symplfying large root problems? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #286659 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=286659\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Simplifying Square-Root Terms<BR>\n" );
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document.write( "To simplify a square root, you \"take out\" anything that is a \"perfect square\"; that is, you take out front anything that has two copies of the same factor:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%29=sqrt%284%5E2%29=4 ALIGN=MIDDLE  ALT=\"sqrt%2816%29=sqrt%284%5E2%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "When you solve the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=+4 ALIGN=MIDDLE  ALT=\"x%5E2+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, you are trying to find all possible values that might have been squared to get 4. But when you are just simplifying the expression<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%284%29 ALIGN=MIDDLE  ALT=\"+sqrt%284%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the ONLY answer is \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\"; this <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive+ ALIGN=MIDDLE  ALT=\"positive+\"   DISABLED_style= \"max-width:90%; height:auto;\" >result is called the \"<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=principal ALIGN=MIDDLE  ALT=\"principal\"   DISABLED_style= \"max-width:90%; height:auto;\" >\" <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root ALIGN=MIDDLE  ALT=\"root\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "Other roots, such as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, can be defined using graduate-school topics like \"complex analysis\" and \"branch functions\".\r<BR>\n" );
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document.write( "2.<BR>\n" );
document.write( "Sometimes the argument of a radical is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=not ALIGN=MIDDLE  ALT=\"not\"   DISABLED_style= \"max-width:90%; height:auto;\" > a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=perfect ALIGN=MIDDLE  ALT=\"perfect\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+square ALIGN=MIDDLE  ALT=\"+square\"   DISABLED_style= \"max-width:90%; height:auto;\" >, but it may \"contain\" a square amongst its factors. <BR>\n" );
document.write( "To simplify, you need to factor the argument and \"take out\" anything that is a square; you find anything you've got a pair of inside the radical, and you <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=move ALIGN=MIDDLE  ALT=\"move\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+it ALIGN=MIDDLE  ALT=\"+it\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+out+ ALIGN=MIDDLE  ALT=\"+out+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=front ALIGN=MIDDLE  ALT=\"front\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "To do this, you use the fact that you can switch between the multiplication of roots and the root of a multiplication. In other words, radicals can be manipulated similarly to powers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28ab%29%5En=a%5En%2Ab%5En+ ALIGN=MIDDLE  ALT=\"%28ab%29%5En=a%5En%2Ab%5En+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%28n%2Cab%29=root%28n%2Ca%29%2Aroot%28n%2Cb%29 ALIGN=MIDDLE  ALT=\"root%28n%2Cab%29=root%28n%2Ca%29%2Aroot%28n%2Cb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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