document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1015324>Question 1015324</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello<BR>\n" );
document.write( "Help I hope I got the right sign looks like a check mark, trying to multiply and simplify and show my work please.\r<BR>\n" );
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document.write( " &#8730;3x^5&#8730; 18x^6\r<BR>\n" );
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document.write( "Thanks Betty </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #631695 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=631695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i think you want sqrt(3x^5) * sqrt(18x^6)\r<BR>\n" );
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document.write( "in general, sqrt(a) * sqrt(b) is equal to sqrt(a*b)\r<BR>\n" );
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document.write( "for example:\r<BR>\n" );
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document.write( "sqrt(4) * sqrt(16) = sqrt(4*16) = sqrt(64) = 8\r<BR>\n" );
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document.write( "sqrt(4) = 2 and sqrt(16) = 4 so sqrt(4) * sqrt(16) = 2*4 = 8\r<BR>\n" );
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document.write( "the answers are the same, so sqrt(4) * sqrt(16) = sqrt(4*16)\r<BR>\n" );
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document.write( "so, your solution becomes:\r<BR>\n" );
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document.write( "sqrt(3x^5) * sqrt(18x^6) = sqrt(3x^5 * 18x^6) = sqrt(54*x^11) = 3x^5*sqrt(6x)\r<BR>\n" );
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document.write( "the simplification process went like this:\r<BR>\n" );
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document.write( "sqrt(54*x^11) = sqrt(6*9*x^10*x)\r<BR>\n" );
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document.write( "since sqrt(9) = 3, then the expression becomes 3*sqrt(6*x^10*x)\r<BR>\n" );
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document.write( "since sqrt(x^10) = x^5, then the expression becomes 3*x^5*sqrt(6x)\r<BR>\n" );
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document.write( "why is sqrt(x^10) = x^5?\r<BR>\n" );
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document.write( "because (x^5)^2 = x^(5*2) = x^10.\r<BR>\n" );
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document.write( "the basic procedure is to remove from under the square root sign, all the perfect squares you can find.\r<BR>\n" );
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document.write( "sqrt(9) is a perfect square, so you remove it from under the squareroot sign and place it outside the square root sign because sqrt(9) = 3\r<BR>\n" );
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document.write( "sqrt(9) = 3\r<BR>\n" );
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document.write( "sqrt(9x) = 3sqrt(x)\r<BR>\n" );
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document.write( "the x is not a perfect square so it remains.<BR>\n" );
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