document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=151532>Question 151532</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the sqrt of 30,875? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #111391 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=111391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2830875%29 ALIGN=MIDDLE  ALT=\"sqrt%2830875%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 30875\r<BR>\n" );
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document.write( "Factors:\r<BR>\n" );
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document.write( "1, 5, 13, 19, 25, 65, 95, 125, 247, 325, 475, 1235, 1625, 2375, 6175, 30875\r<BR>\n" );
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document.write( "Notice how 25 is the largest perfect square, so lets factor 30875 into 25*1235\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2A1235%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2A1235%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 30875 into 25*1235\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29%2Asqrt%281235%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29%2Asqrt%281235%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=5%2Asqrt%281235%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%281235%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect square 25 to get 5 <BR>\n" );
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document.write( "So the expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2830875%29 ALIGN=MIDDLE  ALT=\"sqrt%2830875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2Asqrt%281235%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%281235%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "Notice if we evaluate the square root of 30875 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%2830875%29=175.712833908056 ALIGN=MIDDLE  ALT=\"sqrt%2830875%29=175.712833908056\"   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=5%2Asqrt%281235%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%281235%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=5%2Asqrt%281235%29=175.712833908056 ALIGN=MIDDLE  ALT=\"5%2Asqrt%281235%29=175.712833908056\"   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%2830875%29=5%2Asqrt%281235%29 ALIGN=MIDDLE  ALT=\"sqrt%2830875%29=5%2Asqrt%281235%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this verifies our answer  </SPAN>\n" );
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