document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=248009>Question 248009</A>: <I><SPAN STYLE=\"word-break: break-all;\">  Simplify by factoring. &#8730;(245k^7 q^8 ) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #180842 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=180842\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28245%2Ak%5E7%2Aq%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%28245%2Ak%5E7%2Aq%5E8%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%2849%2A5%2Ak%5E7%2Aq%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%2A5%2Ak%5E7%2Aq%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=245 ALIGN=MIDDLE  ALT=\"245\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49%2A5 ALIGN=MIDDLE  ALT=\"49%2A5\"   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%2849%2A5%2Ak%5E2%2Ak%5E2%2Ak%5E2%2Ak%2Aq%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%2A5%2Ak%5E2%2Ak%5E2%2Ak%5E2%2Ak%2Aq%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E7 ALIGN=MIDDLE  ALT=\"k%5E7\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2%2Ak%5E2%2Ak%5E2%2Ak ALIGN=MIDDLE  ALT=\"k%5E2%2Ak%5E2%2Ak%5E2%2Ak\"   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%2849%2A5%2Ak%5E2%2Ak%5E2%2Ak%5E2%2Ak%2Aq%5E2%2Aq%5E2%2Aq%5E2%2Aq%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%2A5%2Ak%5E2%2Ak%5E2%2Ak%5E2%2Ak%2Aq%5E2%2Aq%5E2%2Aq%5E2%2Aq%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E8 ALIGN=MIDDLE  ALT=\"q%5E8\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2%2Aq%5E2%2Aq%5E2%2Aq%5E2 ALIGN=MIDDLE  ALT=\"q%5E2%2Aq%5E2%2Aq%5E2%2Aq%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%2849%29%2Asqrt%285%29%2Asqrt%28k%5E2%29%2Asqrt%28k%5E2%29%2Asqrt%28k%5E2%29%2Asqrt%28k%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29 ALIGN=MIDDLE   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=7%2Asqrt%285%29%2Asqrt%28k%5E2%29%2Asqrt%28k%5E2%29%2Asqrt%28k%5E2%29%2Asqrt%28k%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=49 ALIGN=MIDDLE  ALT=\"49\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7 ALIGN=MIDDLE  ALT=\"7\"   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=7%2Asqrt%285%29%2Ak%2Ak%2Ak%2Asqrt%28k%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29%2Asqrt%28q%5E2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k%5E2 ALIGN=MIDDLE  ALT=\"k%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=k ALIGN=MIDDLE  ALT=\"k\"   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=7%2Asqrt%285%29%2Ak%2Ak%2Ak%2Asqrt%28k%29%2Aq%2Aq%2Aq%2Aq ALIGN=MIDDLE  ALT=\"7%2Asqrt%285%29%2Ak%2Ak%2Ak%2Asqrt%28k%29%2Aq%2Aq%2Aq%2Aq\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q%5E2 ALIGN=MIDDLE  ALT=\"q%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q ALIGN=MIDDLE  ALT=\"q\"   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=7k%5E3q%5E4%2Asqrt%285k%29 ALIGN=MIDDLE  ALT=\"7k%5E3q%5E4%2Asqrt%285k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange and multiply the terms.\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%28245%2Ak%5E7%2Aq%5E8%29 ALIGN=MIDDLE  ALT=\"sqrt%28245%2Ak%5E7%2Aq%5E8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7k%5E3q%5E4%2Asqrt%285k%29 ALIGN=MIDDLE  ALT=\"7k%5E3q%5E4%2Asqrt%285k%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%28245%2Ak%5E7%2Aq%5E8%29=7k%5E3q%5E4%2Asqrt%285k%29 ALIGN=MIDDLE  ALT=\"sqrt%28245%2Ak%5E7%2Aq%5E8%29=7k%5E3q%5E4%2Asqrt%285k%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is non-negative.<BR>\n" );
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