document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118551>Question 118551</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expression.\r<BR>\n" );
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document.write( "1a) square root of 54<BR>\n" );
document.write( "1b)square root of 72<BR>\n" );
document.write( "1c) square root of 5/9<BR>\n" );
document.write( "1d) square root of 7/36<BR>\n" );
document.write( "1e) square root of 9/11<BR>\n" );
document.write( "1f)square root of 9/25 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86712 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=86712\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first three to show you how to do these problems\r<BR>\n" );
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document.write( "1a)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2854%29 ALIGN=MIDDLE  ALT=\"sqrt%2854%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 54\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 3, 6, 9, 18, 27, 54\r<BR>\n" );
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document.write( "Notice how 9 is the largest perfect square, so lets factor 54 into 9*6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%2A6%29 ALIGN=MIDDLE  ALT=\"sqrt%289%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 54 into 9*6<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%289%29%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%289%29%2Asqrt%286%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%286%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%286%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%2854%29 ALIGN=MIDDLE  ALT=\"sqrt%2854%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%286%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 54 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%2854%29=7.34846922834953 ALIGN=MIDDLE  ALT=\"sqrt%2854%29=7.34846922834953\"   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%286%29 ALIGN=MIDDLE  ALT=\"3%2Asqrt%286%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%286%29=7.34846922834953 ALIGN=MIDDLE  ALT=\"3%2Asqrt%286%29=7.34846922834953\"   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%2854%29=3%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%2854%29=3%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer \r<BR>\n" );
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document.write( "1b)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2872%29 ALIGN=MIDDLE  ALT=\"sqrt%2872%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 72\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72\r<BR>\n" );
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document.write( "Notice how 36 is the largest perfect square, so lets factor 72 into 36*2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2A2%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 72 into 36*2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%29%2Asqrt%282%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=6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 36 to get 6 <BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2872%29 ALIGN=MIDDLE  ALT=\"sqrt%2872%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%282%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 72 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%2872%29=8.48528137423857 ALIGN=MIDDLE  ALT=\"sqrt%2872%29=8.48528137423857\"   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=6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%282%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=6%2Asqrt%282%29=8.48528137423857 ALIGN=MIDDLE  ALT=\"6%2Asqrt%282%29=8.48528137423857\"   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%2872%29=6%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2872%29=6%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer \r<BR>\n" );
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document.write( "1c)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2F9%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2F9%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%285%29%2Fsqrt%289%29 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2Fsqrt%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 9 to get 3\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%2F9%29 ALIGN=MIDDLE  ALT=\"sqrt%285%2F9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29%2F3 ALIGN=MIDDLE  ALT=\"sqrt%285%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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