document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=176930>Question 176930</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How would yiou simplify the following (assuming that the value of each variable is positive):\r<BR>\n" );
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document.write( "(30x^3)^(1/2)&#8729;&#8730;6x^5y^2z^3\r<BR>\n" );
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document.write( "I have a test tomorrow and myself and most of the people in my algebra class are still extremely confused. Please, please, please, help me with this and explain in full detail if possible! You're help would be very much appreciated!<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 #131980 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=131980\">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=%2830x%5E3%29%5E%281%2F2%29%2Asqrt%286x%5E5%2Ay%5E2%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"%2830x%5E3%29%5E%281%2F2%29%2Asqrt%286x%5E5%2Ay%5E2%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%2830x%5E3%29%2Asqrt%286x%5E5%2Ay%5E2%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"sqrt%2830x%5E3%29%2Asqrt%286x%5E5%2Ay%5E2%2Az%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert to radical notation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2830x%5E3%29%286x%5E5%2Ay%5E2%2Az%5E3%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2830x%5E3%29%286x%5E5%2Ay%5E2%2Az%5E3%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%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%29 ALIGN=MIDDLE  ALT=\"sqrt%28x%29%2Asqrt%28y%29=sqrt%28x%2Ay%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%28180%2Ax%5E8%2Ay%5E2%2Az%5E3%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28180%2Ax%5E8%2Ay%5E2%2Az%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2A5%2Ax%5E8%2Ay%5E2%2Az%5E3%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2A5%2Ax%5E8%2Ay%5E2%2Az%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor 180 into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36%2A5 ALIGN=MIDDLE  ALT=\"36%2A5\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: one factor is a perfect square)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2A5%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Az%5E3%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2A5%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Az%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <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;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E4%2Ax%5E4=x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2 ALIGN=MIDDLE  ALT=\"x%5E4%2Ax%5E4=x%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (note: the goal is to get \"x\" with an exponent of 2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%2A5%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Az%5E2%2Az%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%2A5%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ax%5E2%2Ay%5E2%2Az%5E2%2Az%29%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%5E3=z%5E2%2Az ALIGN=MIDDLE  ALT=\"z%5E3=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%2836%29%2Asqrt%285%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the square root.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%285%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of 36 to get 6\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Asqrt%285%29%2Ax%2Ax%2Ax%2Ax%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%29%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%285%29%2Ax%2Ax%2Ax%2Ax%2Asqrt%28y%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%29%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=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   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%285%29%2Ax%2Ax%2Ax%2Ax%2Ay%2Asqrt%28z%5E2%29%2Asqrt%28z%29%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%285%29%2Ax%2Ax%2Ax%2Ax%2Ay%2Asqrt%28z%5E2%29%2Asqrt%28z%29%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=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=6%2Asqrt%285%29%2Ax%2Ax%2Ax%2Ax%2Ay%2Az%2Asqrt%28z%29%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%285%29%2Ax%2Ax%2Ax%2Ax%2Ay%2Az%2Asqrt%28z%29%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=6%2Asqrt%285%29%2Ax%5E4%2Ay%2Az%2Asqrt%28z%29%29 ALIGN=MIDDLE  ALT=\"6%2Asqrt%285%29%2Ax%5E4%2Ay%2Az%2Asqrt%28z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2Ax%5E4%2Ay%2Az%2Asqrt%285z%29%29 ALIGN=MIDDLE  ALT=\"6%2Ax%5E4%2Ay%2Az%2Asqrt%285z%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Recombine the roots.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the expression\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830x%5E3%29%5E%281%2F2%29%2Asqrt%286x%5E5%2Ay%5E2%2Az%5E3%29 ALIGN=MIDDLE  ALT=\"%2830x%5E3%29%5E%281%2F2%29%2Asqrt%286x%5E5%2Ay%5E2%2Az%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "completely simplifies to\r<BR>\n" );
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document.write( "In other words, \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2830x%5E3%29%5E%281%2F2%29%2Asqrt%286x%5E5%2Ay%5E2%2Az%5E3%29=6x%5E4%2Ay%2Az%2Asqrt%285z%29 ALIGN=MIDDLE  ALT=\"%2830x%5E3%29%5E%281%2F2%29%2Asqrt%286x%5E5%2Ay%5E2%2Az%5E3%29=6x%5E4%2Ay%2Az%2Asqrt%285z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > where every variable is positive. </SPAN>\n" );
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