document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=288382>Question 288382</A>: <I><SPAN STYLE=\"word-break: break-all;\"> write &#8730;45 in the form k&#8730;5, where k is an integer  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #209034 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=209034\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <TABLE  BORDER=1>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=simplifying_square_roots.solver>Simplifying Square Roots (whole numbers only)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT><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<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.<BR>\n" );
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document.write( "  So let's list the factors of 45<BR>\n" );
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document.write( "  Factors:<BR>\n" );
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document.write( "  1, 3, 5, 9, 15, 45<BR>\n" );
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document.write( "  Notice how 9 is the largest perfect square, so lets 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%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;\" ><BR>\n" );
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document.write( "  Check:<BR>\n" );
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document.write( "  Notice if we evaluate the square root of 45 with a calculator we get<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;\" ><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<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;\" ><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  </TD></TR>\n" );
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document.write( "Since <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;\" >, this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k=3 ALIGN=MIDDLE  ALT=\"k=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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