document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=37794>Question 37794</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify the radical  . Assume that all variables represent positive numbers. \r<BR>\n" );
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document.write( "square root 8xy^2 <BR>\n" );
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document.write( "square root 5xy\r<BR>\n" );
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document.write( "Explain in detail please?<BR>\n" );
document.write( "Thank you<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23329 by </B><A HREF=/tutors/aboutme.mpl?userid=junior403><B>junior403(76)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=junior403><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=23329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> So we need to simplify the radical...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288xy%5E2%29%2F+sqrt%285xy%29%29+ ALIGN=MIDDLE  ALT=\"sqrt%288xy%5E2%29%2F+sqrt%285xy%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "According to the quotient rule for radicals we need to eliminate the radical sign in the denominator by rationalizing the expression (simply multiplying both the numerator and the denominator by the denominator)Thus creating a square root of a square.<BR>\n" );
document.write( "Sounds confusing but its really simple...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%288xy%5E2%29%2F+sqrt%285xy%29%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%288xy%5E2%29%2F+sqrt%285xy%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%285xy%29%2F+sqrt%285xy%29%29 ALIGN=MIDDLE  ALT=\"%28sqrt%285xy%29%2F+sqrt%285xy%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2840x%5E2y%5E3%29%2F+sqrt%28%285xy%29%29%5E2%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%2840x%5E2y%5E3%29%2F+sqrt%28%285xy%29%29%5E2%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%2840x%5E2y%5E3%29%2F+5xy%29+ ALIGN=MIDDLE  ALT=\"%28sqrt%2840x%5E2y%5E3%29%2F+5xy%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we just have to simplify the numerator...<BR>\n" );
document.write( "40 = 10 * 4 and 4 is a square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2 ALIGN=MIDDLE  ALT=\"2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >so it comes out from under the radical as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt+%2810x%5E2y%5E3%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt+%2810x%5E2y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The same with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > comes out as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2Asqrt+%2810y%5E3%29 ALIGN=MIDDLE  ALT=\"2x%2Asqrt+%2810y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3 ALIGN=MIDDLE  ALT=\"y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > comes out as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2Asqrt+%2810y%29 ALIGN=MIDDLE  ALT=\"2xy%2Asqrt+%2810y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we now have...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2xy%2Asqrt%2810y%29%2F+5xy%29+ ALIGN=MIDDLE  ALT=\"2xy%2Asqrt%2810y%29%2F+5xy%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And this can be reduced further by canceling the xy variables...<BR>\n" );
document.write( "The final result is...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%2810y%29%2F+5%29+ ALIGN=MIDDLE  ALT=\"2%2Asqrt%2810y%29%2F+5%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <BR>\n" );
document.write( "I hope this helps!<BR>\n" );
document.write( "Good Luck!\r<BR>\n" );
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