document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=189994>Question 189994</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/1602773033/algebrahomeworkh>Saxon Algebra 2</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the expression.\r<BR>\n" );
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document.write( "Square root 75 * square root 6\r<BR>\n" );
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document.write( "How would you simplify this? Please help! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #142569 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=142569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2875%29%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%2875%29%2Asqrt%286%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%2875%2A6%29 ALIGN=MIDDLE  ALT=\"sqrt%2875%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29\"   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=sqrt%28450%29 ALIGN=MIDDLE  ALT=\"sqrt%28450%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "Now 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 450\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, 450\r<BR>\n" );
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document.write( "Notice how 225 is the largest perfect square (since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%5E2=225 ALIGN=MIDDLE  ALT=\"15%5E2=225\"   DISABLED_style= \"max-width:90%; height:auto;\" >), so lets factor 450 into 225*2\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28225%2A2%29 ALIGN=MIDDLE  ALT=\"sqrt%28225%2A2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 450 into 225*2<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28225%29%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%28225%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=15%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 225 to get 15 <BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28450%29 ALIGN=MIDDLE  ALT=\"sqrt%28450%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This consequently means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2875%29%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%2875%29%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"15%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as well\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2875%29%2Asqrt%286%29=15%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"sqrt%2875%29%2Asqrt%286%29=15%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
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