document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=162013>Question 162013</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is from a worksheet.  I have 2 questions that i'm not sure on.<BR>\n" );
document.write( "Direction say simplify.  Assume that no denominator equals 0.<BR>\n" );
document.write( "1.  sq. root 16x^2y^4<BR>\n" );
document.write( "2.  sq root 12-sq root 18+3sq root 50+sq root 75.<BR>\n" );
document.write( "Sorry i don't have a sq. root sign on my computer<BR>\n" );
document.write( "Please. help<BR>\n" );
document.write( "Thanks<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 #119409 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=119409\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1)\r<BR>\n" );
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document.write( "For these type of problems, it is <b>crucial</b> to remember that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29=x ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%3E=0 ALIGN=MIDDLE  ALT=\"x%3E=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (ie it's not negative)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816x%5E2y%5E4%29 ALIGN=MIDDLE  ALT=\"sqrt%2816x%5E2y%5E4%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%284%5E2%2Ax%5E2y%5E4%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2%2Ax%5E2y%5E4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16 ALIGN=MIDDLE  ALT=\"16\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2 ALIGN=MIDDLE  ALT=\"4%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%284%5E2%2Ax%5E2%28y%5E2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2%2Ax%5E2%28y%5E2%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E4 ALIGN=MIDDLE  ALT=\"y%5E4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%5E2%29%5E2 ALIGN=MIDDLE  ALT=\"%28y%5E2%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=sqrt%284%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28%28y%5E2%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2%29%2Asqrt%28x%5E2%29%2Asqrt%28%28y%5E2%29%5E2%29\"   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=4xy%5E2 ALIGN=MIDDLE  ALT=\"4xy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Use the formula above to simplify each square root. So in this case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284%5E2%29=4 ALIGN=MIDDLE  ALT=\"sqrt%284%5E2%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x%5E2%29=x ALIGN=MIDDLE  ALT=\"sqrt%28x%5E2%29=x\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%28y%5E2%29%5E2%29=y%5E2 ALIGN=MIDDLE  ALT=\"sqrt%28%28y%5E2%29%5E2%29=y%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816x%5E2y%5E4%29=4xy%5E2 ALIGN=MIDDLE  ALT=\"sqrt%2816x%5E2y%5E4%29=4xy%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > every variable is nonnegative\r<BR>\n" );
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document.write( "2)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29-sqrt%2818%29%2B3%2Asqrt%2850%29%2Bsqrt%2875%29 ALIGN=MIDDLE  ALT=\"sqrt%2812%29-sqrt%2818%29%2B3%2Asqrt%2850%29%2Bsqrt%2875%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given expression\r<BR>\n" );
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document.write( "Now we must factor each number in the square roots into two number where one MUST be 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%284%2A3%29-sqrt%289%2A2%29%2B3%2Asqrt%2825%2A2%29%2Bsqrt%2825%2A3%29 ALIGN=MIDDLE  ALT=\"sqrt%284%2A3%29-sqrt%289%2A2%29%2B3%2Asqrt%2825%2A2%29%2Bsqrt%2825%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2A3 ALIGN=MIDDLE  ALT=\"4%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18 ALIGN=MIDDLE  ALT=\"18\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2A2 ALIGN=MIDDLE  ALT=\"9%2A2\"   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;\" >. Factor <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=75 ALIGN=MIDDLE  ALT=\"75\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25%2A3 ALIGN=MIDDLE  ALT=\"25%2A3\"   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%284%29%2Asqrt%283%29-sqrt%289%29%2Asqrt%282%29%2B3%2Asqrt%2825%29%2Asqrt%282%29%2Bsqrt%2825%29%2Asqrt%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Break p the square roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%5E2%29%2Asqrt%283%29-sqrt%283%5E2%29%2Asqrt%282%29%2B3%2Asqrt%285%5E2%29%2Asqrt%282%29%2Bsqrt%285%5E2%29%2Asqrt%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%5E2 ALIGN=MIDDLE  ALT=\"2%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2 ALIGN=MIDDLE  ALT=\"3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%5E2 ALIGN=MIDDLE  ALT=\"5%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=2%2Asqrt%283%29-3%2Asqrt%282%29%2B3%2A5%2Asqrt%282%29%2B5%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29-3%2Asqrt%282%29%2B3%2A5%2Asqrt%282%29%2B5%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of the perfect squares to simplify the square roots. So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%5E2%29=2 ALIGN=MIDDLE  ALT=\"sqrt%282%5E2%29=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%283%5E2%29=3 ALIGN=MIDDLE  ALT=\"sqrt%283%5E2%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%5E2%29=5 ALIGN=MIDDLE  ALT=\"sqrt%285%5E2%29=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=2%2Asqrt%283%29-3%2Asqrt%282%29%2B15%2Asqrt%282%29%2B5%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%283%29-3%2Asqrt%282%29%2B15%2Asqrt%282%29%2B5%2Asqrt%283%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=%28-3%2Asqrt%282%29%2B15%2Asqrt%282%29%29%2B%282%2Asqrt%283%29%2B5%2Asqrt%283%29%29 ALIGN=MIDDLE  ALT=\"%28-3%2Asqrt%282%29%2B15%2Asqrt%282%29%29%2B%282%2Asqrt%283%29%2B5%2Asqrt%283%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group the common terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12%2Asqrt%282%29%2B7%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"12%2Asqrt%282%29%2B7%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine the common terms.\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2812%29-sqrt%2818%29%2B3%2Asqrt%2850%29%2Bsqrt%2875%29=12%2Asqrt%282%29%2B7%2Asqrt%283%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >  </SPAN>\n" );
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