document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=468681>Question 468681</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Divide Then simplify by taking roots, if possible Assume that all expressions under radical represent positive numbers<BR>\n" );
document.write( "V63xy^3 / V9x\r<BR>\n" );
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document.write( "the v's are square root symbols and ^means it is raising to that power this is also a fraction, so it is the square root of 63xy^3 (numerator) over the square root of 9x (denominator) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #321577 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=321577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In algebra.com, square root of a number is officially shown as sqrt(x).<BR>\n" );
document.write( "any root of a number greater than that would be shown as root(n,x) where n is the power of the root and x is the number.<BR>\n" );
document.write( "for example:<BR>\n" );
document.write( "square root of 2 would be shown as sqrt(2)<BR>\n" );
document.write( "cube root of 2 would be shown as root(3,2)<BR>\n" );
document.write( "5th root of 2 would be shown as root 5,2)<BR>\n" );
document.write( "etc.<BR>\n" );
document.write( "If you are going to continue to use the V symbol, then enclose the expression that is within the root sign in parentheses.<BR>\n" );
document.write( "Your problem could be restated as:<BR>\n" );
document.write( "V(63xy^3) / V(9x)<BR>\n" );
document.write( "Algebra.com notation would show it as:<BR>\n" );
document.write( "sqrt(63xy^3) / sqrt(9x)<BR>\n" );
document.write( "If you put 3 curly brackets in front and 3 curly brackets in back, then the algebra.com formula generator would show it as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2863xy%5E3%29+%2F+sqrt%289x%29 ALIGN=MIDDLE  ALT=\"sqrt%2863xy%5E3%29+%2F+sqrt%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The front curly brackets look like {.<BR>\n" );
document.write( "The back curly brackets look like }.<BR>\n" );
document.write( "On your keyboard, they would be to the right of the P.<BR>\n" );
document.write( "They would be Shift [ and Shift ] (upper case letters on those keys).<BR>\n" );
document.write( "That's on my keyboard which is a Toshiba.  Your keyboard might be different but possibly not.<BR>\n" );
document.write( "Anyway, back to your problem.<BR>\n" );
document.write( "you have sqrt(63xy^3) / sqrt(9x).<BR>\n" );
document.write( "This is equivalent to sqrt(63xy^3/9x).<BR>\n" );
document.write( "The x in the numerator and the x in the denominator cancel out and you are left with sqrt(63y^3/9)<BR>\n" );
document.write( "9 goes into 63 seven times and you are left with sqrt(7y^3)<BR>\n" );
document.write( "y^3 is equivalent to y^2 * y which means you can take the sqrt of y^2 and make it a y outside the square root sign to get y*sqrt(7y).<BR>\n" );
document.write( "That should be your final answer.<BR>\n" );
document.write( "sqrt(63xy^3) / sqrt(9x) is equivalent to y*sqrt(7y).<BR>\n" );
document.write( "In algebra.com formula generator format, that would look like:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2863xy%5E3%29+%2F+sqrt%289x%29 ALIGN=MIDDLE  ALT=\"sqrt%2863xy%5E3%29+%2F+sqrt%289x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%2Asqrt%287y%29 ALIGN=MIDDLE  ALT=\"y%2Asqrt%287y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "I have confirmed that the original equation gives you the same answer as the final equation by substituting a value for x and a value for y and solving both the original equation and the final equation.<BR>\n" );
document.write( "Since the answer in both cases came out the same, I am reasonably confident I did it right.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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