document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=177297>Question 177297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am unsure how to solve this problem:<BR>\n" );
document.write( "z sqrt 50zu^2- 8u sqrt 2z^3<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 #132450 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=132450\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First, simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850zu%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2850zu%5E2%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%2850%2Az%2Au%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%2Az%2Au%5E2%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%2825%2A2%2Az%2Au%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2A2%2Az%2Au%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50 ALIGN=MIDDLE  ALT=\"50\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2A2 ALIGN=MIDDLE  ALT=\"25%2A2\"   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%2825%29%2Asqrt%282%29%2Asqrt%28z%29%2Asqrt%28u%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29%2Asqrt%282%29%2Asqrt%28z%29%2Asqrt%28u%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=5%2Asqrt%282%29%2Asqrt%28z%29%2Asqrt%28u%5E2%29 ALIGN=MIDDLE  ALT=\"5%2Asqrt%282%29%2Asqrt%28z%29%2Asqrt%28u%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=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5 ALIGN=MIDDLE  ALT=\"5\"   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=5%2Asqrt%282%29%2Asqrt%28z%29%2Au ALIGN=MIDDLE  ALT=\"5%2Asqrt%282%29%2Asqrt%28z%29%2Au\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u%5E2 ALIGN=MIDDLE  ALT=\"u%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   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=5u%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"5u%2Asqrt%282z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange and combine the terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2850%2Az%2Au%5E2%29=5u%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"sqrt%2850%2Az%2Au%5E2%29=5u%2Asqrt%282z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive.\r<BR>\n" );
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document.write( "Now let's simplify <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2Az%5E3%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%282%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2Az%5E3%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%282%2Az%5E2%2Az%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2Az%5E2%2Az%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E3 ALIGN=MIDDLE  ALT=\"z%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%5E2%2Az ALIGN=MIDDLE  ALT=\"z%5E2%2Az\"   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%282%29%2Asqrt%28z%5E2%29%2Asqrt%28z%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Asqrt%28z%5E2%29%2Asqrt%28z%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=sqrt%282%29%2Az%2Asqrt%28z%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Az%2Asqrt%28z%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=z%5E2 ALIGN=MIDDLE  ALT=\"z%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   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=z%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"z%2Asqrt%282z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange and combine the terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%2Az%5E3%29=z%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"sqrt%282%2Az%5E3%29=z%2Asqrt%282z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive.\r<BR>\n" );
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document.write( "So \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "simplifies to \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z%2A5u%2Asqrt%282z%29-8u%2Az%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"z%2A5u%2Asqrt%282z%29-8u%2Az%2Asqrt%282z%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=5uz%2Asqrt%282z%29-8uz%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"5uz%2Asqrt%282z%29-8uz%2Asqrt%282z%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%282z%29%2A%285uz-8uz%29 ALIGN=MIDDLE  ALT=\"sqrt%282z%29%2A%285uz-8uz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282z%29 ALIGN=MIDDLE  ALT=\"sqrt%282z%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%282z%29%2A%28-3uz%29 ALIGN=MIDDLE  ALT=\"sqrt%282z%29%2A%28-3uz%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3uz%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"-3uz%2Asqrt%282z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange 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=z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > completely simplifies to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-3uz%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"-3uz%2Asqrt%282z%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=z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29=-3uz%2Asqrt%282z%29 ALIGN=MIDDLE  ALT=\"z%2Asqrt%2850zu%5E2%29-8u%2Asqrt%282%2Az%5E3%29=-3uz%2Asqrt%282z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive. </SPAN>\n" );
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