document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201014>Question 1201014</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify -2√180u³v^6\r<BR>\n" );
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document.write( "I know what the answer is but I don't understand the u³ and how is breaks down because 2 doesn't go in evenly to the exponent 3? If you pull a \"u\" out and leave one under the square root, you have a 1 \"u\" left over. Where is it? What am I missing? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835245 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835245\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you have a u^3 under the dequare root sign.<BR>\n" );
document.write( "you can pull out a u^2 and you have to leave a u under the squar root sign.<BR>\n" );
document.write( "with the v^6,  you can pull out 3 v^2.<BR>\n" );
document.write( "the result is -2 * u * v^3 * sqrt(180 * u)<BR>\n" );
document.write( "the sqrt(180) becomes sqrt(3 * 3 * 20), so  you can pull out a 3 to get:<BR>\n" );
document.write( "-2 * u * v^3 * 3 * sqrt(20 * u)<BR>\n" );
document.write( "this simplifies to -6 * u * v^3 * sqrt(20 * u).<BR>\n" );
document.write( "you can test to see if you did this correctly by randomly assigning a value fo u and v.<BR>\n" );
document.write( "i chose 3 for u and 5 for v.<BR>\n" );
document.write( "the original expression becomes -2 * sqrt(180 * 3^3 * 5^6) which results in - 17428.42506.<BR>\n" );
document.write( "the final expression becomes -6 * 3 * 5^3 * sqrt(20 * 3) = -17428.42506.<BR>\n" );
document.write( "the answers are the same which incidcates that the simplification is correct.\r<BR>\n" );
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document.write( "note that 20 is equal to 2 * 2 * 5, so that can also be simplified a little further to get:<BR>\n" );
document.write( "-6 * u * v^3 * sqrt(2 * 2 * 5 * u) which becomes:<BR>\n" );
document.write( "-6 * 2 * u * v^3 * sqrt(5 * u) which becomes:<BR>\n" );
document.write( "-12 * u * v^3 * sqrt(5 * u).<BR>\n" );
document.write( "using u = 3 and v = 5, i get -17428.42506, indicating the simplification is still good.\r<BR>\n" );
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document.write( "let me know if this explains what you were asking and if you have any further quetions.<BR>\n" );
document.write( "theo </SPAN>\n" );
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