document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=116821>Question 116821</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is square root of 4x squared menus 20x plus 25 <BR>\n" );
document.write( " and three root of negative 8n to the 12 y to the 9<BR>\n" );
document.write( "i don't understand how to even start these </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #84945 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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/cgi-bin/show-face.mpl?user=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=84945\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Your expressions have a little bit of ambiguity in them, but I think you mean:\r<BR>\n" );
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document.write( "1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284x%5E2-20x%2B25%29 ALIGN=MIDDLE  ALT=\"sqrt%284x%5E2-20x%2B25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C-8n%5E12+%28y%5E9%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C-8n%5E12+%28y%5E9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "1) if you factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-20x%2B25 ALIGN=MIDDLE  ALT=\"4x%5E2-20x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-5%29%282x-5%29 ALIGN=MIDDLE  ALT=\"%282x-5%29%282x-5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (I'll leave it as an exercise for you to verify that is true - Hint: use FOIL).  Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282x-5%29%282x-5%29=%282x-5%29%5E2 ALIGN=MIDDLE  ALT=\"%282x-5%29%282x-5%29=%282x-5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we can say:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284x%5E2-20x%2B25%29=sqrt%28%282x-5%29%5E2%29=2x-5 ALIGN=MIDDLE  ALT=\"sqrt%284x%5E2-20x%2B25%29=sqrt%28%282x-5%29%5E2%29=2x-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "2) Again, let's factor the expression under the radical.  I'm not going to factor it completely, just enough to make it convenient to take the cube root.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8n%5E12+%28y%5E9%29=%28-2%29%28-2%29%28-2%29%28n%5E4%29%28n%5E4%29%28n%5E4%29%28y%5E3%29%28y%5E3%29%28y%5E3%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  (we can say this because we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5Ea%29%28x%5Eb%29=x%5E%28a%2Bb%29 ALIGN=MIDDLE  ALT=\"%28x%5Ea%29%28x%5Eb%29=x%5E%28a%2Bb%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
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document.write( "So, we want <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C%28-2%29%28-2%29%28-2%29%28n%5E4%29%28n%5E4%29%28n%5E4%29%28y%5E3%29%28y%5E3%29%28y%5E3%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "There are three factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-2 ALIGN=MIDDLE  ALT=\"-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we take one of them,<BR>\n" );
document.write( "There are three factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5E4 ALIGN=MIDDLE  ALT=\"n%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we take one of them,<BR>\n" );
document.write( "and there are three factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E3 ALIGN=MIDDLE  ALT=\"y%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so we take one of them, and put them all together:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C-8n%5E12+%28y%5E9%29%29=-2n%5E4%28y%5E3%29 ALIGN=MIDDLE  ALT=\"root%283%2C-8n%5E12+%28y%5E9%29%29=-2n%5E4%28y%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "And you can multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2n%5E4%28y%5E3%29%29%28-2n%5E4%28y%5E3%29%29%28-2n%5E4%28y%5E3%29%29 ALIGN=MIDDLE  ALT=\"%28-2n%5E4%28y%5E3%29%29%28-2n%5E4%28y%5E3%29%29%28-2n%5E4%28y%5E3%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and verify that it equals <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8n%5E12+%28y%5E9%29%29 ALIGN=MIDDLE  ALT=\"-8n%5E12+%28y%5E9%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to check the answer.\r<BR>\n" );
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document.write( "Hope this helps<BR>\n" );
document.write( "John\r<BR>\n" );
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