document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=346670>Question 346670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this Math question:\r<BR>\n" );
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document.write( "sqrt150 - sqrt24 -sqrt54\r<BR>\n" );
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document.write( "Sorry I don't remember how to do the sign for square root on the computer.\r<BR>\n" );
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document.write( "Thank you!!!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #247879 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=247879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't think you are supposed to use a computer or calculator, even if you remember how to use them to find square roots. All computers or calculators can do with most square roots is to find a decimal approximation for the square root.<br><BR>\n" );
document.write( "Instead, I believe your problem is to simplify the expression. Simplifying square roots involves finding perfect square factors of the radicand, if any. (\"Radicand\" is the name for the expression inside a radical (like a square root).) So we will start by looking for perfect square factors in each of the radicands and, if we find them, rewriting the radicands as a product involving these perfect squares:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28150%29+-+sqrt%2824%29+-sqrt%2854%29 ALIGN=MIDDLE  ALT=\"sqrt%28150%29+-+sqrt%2824%29+-sqrt%2854%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%2A6%29+-+sqrt%284%2A6%29+-+sqrt%289%2A6%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%2A6%29+-+sqrt%284%2A6%29+-+sqrt%289%2A6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Next we use a property of radicals, <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;\" >, to separate the perfect squares factors into their own square roots:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825%29%2Asqrt%286%29+-+sqrt%284%29%2Asqrt%286%29+-+sqrt%289%29%2Asqrt%286%29 ALIGN=MIDDLE  ALT=\"sqrt%2825%29%2Asqrt%286%29+-+sqrt%284%29%2Asqrt%286%29+-+sqrt%289%29%2Asqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now we can replace the square roots of the perfect squares:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrt%286%29+-+2sqrt%286%29+-+3sqrt%286%29 ALIGN=MIDDLE  ALT=\"5sqrt%286%29+-+2sqrt%286%29+-+3sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now the square roots have been simplified. Next we simplify the expression as a whole, if possible. It turns out that these are like terms so they can be added/subtracted. (If you have trouble seeing this, perhaps using a temporary variable will help. Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=q+=+sqrt%286%29 ALIGN=MIDDLE  ALT=\"q+=+sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Then the expression becomes: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5q+-+2q+-3q ALIGN=MIDDLE  ALT=\"5q+-+2q+-3q\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This, I hope you can see, is an expression of like terms. And so is the expression with the square roots of 6!)<br><BR>\n" );
document.write( "As it turns out, subtracting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%286%29 ALIGN=MIDDLE  ALT=\"2sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5sqrt%286%29 ALIGN=MIDDLE  ALT=\"5sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > leaves <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%286%29 ALIGN=MIDDLE  ALT=\"3sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just like 5q - 2q  = 3q). And if we then subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%286%29 ALIGN=MIDDLE  ALT=\"3sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > from <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3sqrt%286%29 ALIGN=MIDDLE  ALT=\"3sqrt%286%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > we get 0.<br><BR>\n" );
document.write( "So the simplified expression is zero! </SPAN>\n" );
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