document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=190644>Question 190644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me.<BR>\n" );
document.write( "Simplify. Assume that all variables represent positive real numbers.<BR>\n" );
document.write( "The square root of 3wy^3 times the sqaure root of 12w^2 y\r<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 #143124 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=143124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29 ALIGN=MIDDLE  ALT=\"sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%283wy%5E3%29%2812w%5E2y%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%283wy%5E3%29%2812w%5E2y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the roots using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%29%2Asqrt%28B%29=sqrt%28A%2AB%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%29%2Asqrt%28B%29=sqrt%28A%2AB%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%283%2A12%29%28wy%5E3%2Aw%5E2y%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%283%2A12%29%28wy%5E3%2Aw%5E2y%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836wy%5E3%2Aw%5E2y%29 ALIGN=MIDDLE  ALT=\"sqrt%2836wy%5E3%2Aw%5E2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 3 and 12 to get 36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836w%5E%281%2B2%29y%5E%283%2B1%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2836w%5E%281%2B2%29y%5E%283%2B1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the variable terms by adding the corresponding exponents.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836w%5E3y%5E4%29 ALIGN=MIDDLE  ALT=\"sqrt%2836w%5E3y%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2Aw%5E2%2Aw%2Ay%5E4%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2Aw%5E2%2Aw%2Ay%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E3 ALIGN=MIDDLE  ALT=\"w%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2Aw ALIGN=MIDDLE  ALT=\"w%5E2%2Aw\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2Aw%5E2%2Aw%2Ay%5E2%2Ay%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2Aw%5E2%2Aw%2Ay%5E2%2Ay%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4 ALIGN=MIDDLE  ALT=\"y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2Ay%5E2 ALIGN=MIDDLE  ALT=\"y%5E2%2Ay%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29%2Asqrt%28w%5E2%29%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%29%2Asqrt%28w%5E2%29%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root using the identity <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%2AB%29=sqrt%28A%29%2Asqrt%28B%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%28w%5E2%29%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%28w%5E2%29%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Aw%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29 ALIGN=MIDDLE  ALT=\"6%2Aw%2Asqrt%28w%29%2Asqrt%28y%5E2%29%2Asqrt%28y%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2 ALIGN=MIDDLE  ALT=\"w%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Aw%2Asqrt%28w%29%2Ay%2Ay ALIGN=MIDDLE  ALT=\"6%2Aw%2Asqrt%28w%29%2Ay%2Ay\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2 ALIGN=MIDDLE  ALT=\"y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6wy%5E2%2Asqrt%28w%29 ALIGN=MIDDLE  ALT=\"6wy%5E2%2Asqrt%28w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange and multiply.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29 ALIGN=MIDDLE  ALT=\"sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6wy%5E2%2Asqrt%28w%29 ALIGN=MIDDLE  ALT=\"6wy%5E2%2Asqrt%28w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "In other words, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29=6wy%5E2%2Asqrt%28w%29 ALIGN=MIDDLE  ALT=\"sqrt%283wy%5E3%29%2Asqrt%2812w%5E2y%29=6wy%5E2%2Asqrt%28w%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is non-negative.\r<BR>\n" );
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