document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=150900>Question 150900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Remove the radicals and simplify the following equation<BR>\n" );
document.write( "(x-3)^1/2  +  (2x)^1/2   = 3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #110841 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=110841\">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=%28x-3%29%5E%281%2F2%29+%2B+%282x%29%5E%281%2F2%29=+3 ALIGN=MIDDLE  ALT=\"%28x-3%29%5E%281%2F2%29+%2B+%282x%29%5E%281%2F2%29=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28x-3%29+%2B+sqrt%282x%29=+3 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29+%2B+sqrt%282x%29=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Convert the equation from rational exponent notation 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%28x-3%29+=+3-+sqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%28x-3%29+=+3-+sqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282x%29 ALIGN=MIDDLE  ALT=\"sqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+=+%283-+sqrt%282x%29%29%5E2 ALIGN=MIDDLE  ALT=\"x-3+=+%283-+sqrt%282x%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+=+9-6%2Asqrt%282x%29%2B2x ALIGN=MIDDLE  ALT=\"x-3+=+9-6%2Asqrt%282x%29%2B2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-3+-9-2x=+-6%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"x-3+-9-2x=+-6%2Asqrt%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 9 from both sides. Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-x-12=+-6%2Asqrt%282x%29 ALIGN=MIDDLE  ALT=\"-x-12=+-6%2Asqrt%282x%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=%28-x-12%29%5E2=+36%2A%282x%29 ALIGN=MIDDLE  ALT=\"%28-x-12%29%5E2=+36%2A%282x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-x-12%29%5E2=+72x ALIGN=MIDDLE  ALT=\"%28-x-12%29%5E2=+72x\"   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=x%5E2%2B24x%2B144=+72x ALIGN=MIDDLE  ALT=\"x%5E2%2B24x%2B144=+72x\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B24x%2B144-72x=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B24x%2B144-72x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72x ALIGN=MIDDLE  ALT=\"72x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-48x%2B144=0 ALIGN=MIDDLE  ALT=\"x%5E2-48x%2B144=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-48 ALIGN=MIDDLE  ALT=\"b=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=144 ALIGN=MIDDLE  ALT=\"c=144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-48%29+%2B-+sqrt%28+%28-48%29%5E2-4%281%29%28144%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-48%29+%2B-+sqrt%28+%28-48%29%5E2-4%281%29%28144%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-48 ALIGN=MIDDLE  ALT=\"b=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=144 ALIGN=MIDDLE  ALT=\"c=144\"   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=x+=+%2848+%2B-+sqrt%28+%28-48%29%5E2-4%281%29%28144%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2848+%2B-+sqrt%28+%28-48%29%5E2-4%281%29%28144%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=48 ALIGN=MIDDLE  ALT=\"48\"   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=x+=+%2848+%2B-+sqrt%28+2304-4%281%29%28144%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2848+%2B-+sqrt%28+2304-4%281%29%28144%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-48 ALIGN=MIDDLE  ALT=\"-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   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=x+=+%2848+%2B-+sqrt%28+2304-576+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2848+%2B-+sqrt%28+2304-576+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%28144%29 ALIGN=MIDDLE  ALT=\"4%281%29%28144%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576 ALIGN=MIDDLE  ALT=\"576\"   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=x+=+%2848+%2B-+sqrt%28+1728+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%2848+%2B-+sqrt%28+1728+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=576 ALIGN=MIDDLE  ALT=\"576\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2304 ALIGN=MIDDLE  ALT=\"2304\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1728 ALIGN=MIDDLE  ALT=\"1728\"   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=x+=+%2848+%2B-+sqrt%28+1728+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2848+%2B-+sqrt%28+1728+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   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=x+=+%2848+%2B-+24%2Asqrt%283%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2848+%2B-+24%2Asqrt%283%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root  (note: If you need help with simplifying square roots, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2848%29%2F%282%29+%2B-+%2824%2Asqrt%283%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2848%29%2F%282%29+%2B-+%2824%2Asqrt%283%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the fraction.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24+%2B-+12%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+24+%2B-+12%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24%2B12%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+24%2B12%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24-12%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+24-12%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression.  \r<BR>\n" );
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document.write( "So the possible answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24%2B12%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+24%2B12%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24-12%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+24-12%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "However, if you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24%2B12%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+24%2B12%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the equation will not be true. \r<BR>\n" );
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document.write( "So the only answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24-12%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+24-12%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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