document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=212370>Question 212370</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I’m really confusing with this factoring, Can anyone please help me with step by step? Thank you very much!\r<BR>\n" );
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document.write( "Simplify by factoring.<BR>\n" );
document.write( "1.4*sqrt(405x^8y^10)=?\r<BR>\n" );
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document.write( "2.5*sqrt(64x^12y^15)=?<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 #160399 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=160399\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I'll do the first one to get you going in the right direction.\r<BR>\n" );
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document.write( "# 1\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%28405x%5E8y%5E10%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%28405x%5E8y%5E10%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=4%2Asqrt%28405%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%28405%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%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%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%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=4%2Asqrt%2881%2A5%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%2881%2A5%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 405 into 81*5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%289%5E2%2A5%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%289%5E2%2A5%29%2Asqrt%28x%5E8%29%2Asqrt%28y%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite 81 as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%5E2 ALIGN=MIDDLE  ALT=\"9%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=4%2Asqrt%289%5E2%2A5%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28y%5E10%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%289%5E2%2A5%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28y%5E10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E8 ALIGN=MIDDLE  ALT=\"x%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%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=4%2Asqrt%289%5E2%2A5%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%289%5E2%2A5%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E10 ALIGN=MIDDLE  ALT=\"y%5E10\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E5%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E5%29%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=4%2Asqrt%289%5E2%29%2Asqrt%285%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%289%5E2%29%2Asqrt%285%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the first square root (using that same identity)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A9%2Asqrt%285%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%5E2%29 ALIGN=MIDDLE  ALT=\"4%2A9%2Asqrt%285%29%2Asqrt%28%28x%5E4%29%5E2%29%2Asqrt%28%28y%5E5%29%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=9%5E2 ALIGN=MIDDLE  ALT=\"9%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 9 (notice how the squares and the square roots 'undo' each other).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A9%2Asqrt%285%29%2Ax%5E4%2Asqrt%28%28y%5E5%29%5E2%29 ALIGN=MIDDLE  ALT=\"4%2A9%2Asqrt%285%29%2Ax%5E4%2Asqrt%28%28y%5E5%29%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=%28x%5E4%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%5E4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4 ALIGN=MIDDLE  ALT=\"x%5E4\"   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=4%2A9%2Asqrt%285%29%2Ax%5E4%2Ay%5E5 ALIGN=MIDDLE  ALT=\"4%2A9%2Asqrt%285%29%2Ax%5E4%2Ay%5E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E5%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E5 ALIGN=MIDDLE  ALT=\"y%5E5\"   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=36x%5E4y%5E5%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"36x%5E4y%5E5%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Asqrt%28405x%5E8y%5E10%29=36x%5E4y%5E5%2Asqrt%285%29 ALIGN=MIDDLE  ALT=\"4%2Asqrt%28405x%5E8y%5E10%29=36x%5E4y%5E5%2Asqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is nonnegative. </SPAN>\n" );
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