document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=38208>Question 38208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express the following expression in simplest radical form.  All variables represent positive real numbers.\r<BR>\n" );
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document.write( "SQRT of 27(a^2)b / SQRT of 7(a^3)(b^3) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #23667 by </B><A HREF=/tutors/aboutme.mpl?userid=fractalier><B>fractalier(6550)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=fractalier><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=fractalier><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=23667\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> From<BR>\n" );
document.write( "sqrt27(a^2)b / sqrt7(a^3)(b^3)<BR>\n" );
document.write( "we can make it all one root and then cancel as possible, thus we get<BR>\n" );
document.write( "sqrt[27(a^2)b / 7(a^3)(b^3)] =<BR>\n" );
document.write( "sqrt[27 / 7ab^2] <BR>\n" );
document.write( "From here, we need to rationalize the denominator by multiplying top and bottom by sqrt(7a)/sqrt(7a)...so we have<BR>\n" );
document.write( "sqrt[27 / 7ab^2] * sqrt(7a)/sqrt(7a) =<BR>\n" );
document.write( "sqrt[189a / 49(a^2)(b^2)]<BR>\n" );
document.write( "Now 49(a^2)(b^2) is a perfect square so we can remove it from the root...our final answer is<BR>\n" );
document.write( "sqrt(189a) / 7ab </SPAN>\n" );
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