document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=120559>Question 120559</A>: <I><SPAN STYLE=\"word-break: break-all;\"> simplify the expression\r<BR>\n" );
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document.write( "a)square root of 45<BR>\n" );
document.write( "b)square root of 54<BR>\n" );
document.write( "c)square root of 16/25<BR>\n" );
document.write( "d)square root of 10/32 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #88378 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=88378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do A and C to help you get started\r<BR>\n" );
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document.write( "A)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2845%29 ALIGN=MIDDLE  ALT=\"sqrt%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "The goal of simplifying expressions with square roots is to factor the radicand into a product of two numbers. One of these two numbers must be a perfect square. When you take the square root of this perfect square, you will get a rational number.\r<BR>\n" );
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document.write( "So let's list the factors of 45\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 3, 5, 9, 15, 45\r<BR>\n" );
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document.write( "Notice how 9 is the largest perfect square, so lets factor 45 into 9*5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%2A5%29 ALIGN=MIDDLE  ALT=\"sqrt%289%2A5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 45 into 9*5<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 9 to get 3 <BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2845%29 ALIGN=MIDDLE  ALT=\"sqrt%2845%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "----------------------------<BR>\n" );
document.write( "Check:\r<BR>\n" );
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document.write( "Notice if we evaluate the square root of 45 with a calculator we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2845%29=6.70820393249937 ALIGN=MIDDLE  ALT=\"sqrt%2845%29=6.70820393249937\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "and if we evaluate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%285%29=6.70820393249937 ALIGN=MIDDLE  ALT=\"3%2Asqrt%285%29=6.70820393249937\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This shows that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2845%29=3%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%2845%29=3%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer \r<BR>\n" );
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document.write( "C)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2F25%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2F25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%29%2Fsqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%29%2Fsqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2Fsqrt%2825%29 ALIGN=MIDDLE  ALT=\"%284%29%2Fsqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%29%2F%285%29 ALIGN=MIDDLE  ALT=\"%284%29%2F%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2F25%29=4%2F5 ALIGN=MIDDLE  ALT=\"sqrt%2816%2F25%29=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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