document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98208>Question 98208</A>: <I><SPAN STYLE=\"word-break: break-all;\"> square root of 11(square root of 11 + x square root 22)   \r<BR>\n" );
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document.write( "How do i do this kind of problem?  I am lost it is\r<BR>\n" );
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document.write( "square root of 11 times square root of 11 plus x square root of 22 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71477 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=71477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29%2A%28sqrt%2811%29+%2B+x%2Asqrt%2822%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29%2A%28sqrt%2811%29+%2B+x%2Asqrt%2822%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "This is a problem involving distributed multiplication. It is of the form:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2A%28B+%2B+C%29+=+A%2AB+%2B+A%2AC ALIGN=MIDDLE  ALT=\"A%2A%28B+%2B+C%29+=+A%2AB+%2B+A%2AC\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== call this rule 1<BR>\n" );
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document.write( "Notice that you are just multiplying the term outside the parentheses by each of the terms<BR>\n" );
document.write( "inside the parentheses.<BR>\n" );
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document.write( "What makes this problem a little \"different\" is that it involves multiplication of square roots,<BR>\n" );
document.write( "so you need to know a few rules about those multiplications.  Here are a couple of rules for<BR>\n" );
document.write( "square roots:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%29%2A+sqrt%28A%29+=+A ALIGN=MIDDLE  ALT=\"sqrt%28A%29%2A+sqrt%28A%29+=+A\"   DISABLED_style= \"max-width:90%; height:auto;\" > <=== call this rule 2<BR>\n" );
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document.write( "and:<BR>\n" );
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document.write( "<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;\" > <=== call this rule 3<BR>\n" );
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document.write( "It seems as if this problem involves a lot of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms. But notice that there<BR>\n" );
document.write( "is one term that is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2822%29 ALIGN=MIDDLE  ALT=\"sqrt%2822%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. If we apply rule 3 to that term, we can get a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "from it by doing the following:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2822%29+=+sqrt%282%2A11%29+=+sqrt%282%29%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2822%29+=+sqrt%282%2A11%29+=+sqrt%282%29%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "So in the problem we can replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2822%29 ALIGN=MIDDLE  ALT=\"sqrt%2822%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%282%29%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the problem<BR>\n" );
document.write( "then becomes:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29%2A%28sqrt%2811%29%2B+x%2Asqrt%282%29%2Asqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29%2A%28sqrt%2811%29%2B+x%2Asqrt%282%29%2Asqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now let's apply rule 1. We'll do that by multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > times each of the<BR>\n" );
document.write( "terms in the parentheses to get:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29%2Asqrt%2811%29+%2B+sqrt%2811%29%2Ax%2Asqrt%282%29%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29%2Asqrt%2811%29+%2B+sqrt%2811%29%2Ax%2Asqrt%282%29%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now we can apply rule 2 to both of these terms. The first term is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and rule 2 tells us that the answer is just 11. So substituting 11 into the problem reduces<BR>\n" );
document.write( "the problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+%2B+sqrt%2811%29%2Ax%2Asqrt%282%29%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"11+%2B+sqrt%2811%29%2Ax%2Asqrt%282%29%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Notice now that in the second term there is also a <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29%2Asqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29%2Asqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > involved. Rule<BR>\n" );
document.write( "2 also allows us to replace that product with 11. And this substitution further reduces the<BR>\n" );
document.write( "problem to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11+%2B+11%2Ax%2Asqrt%282%29 ALIGN=MIDDLE  ALT=\"11+%2B+11%2Ax%2Asqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "That's the answer to this problem. I suppose that if you wanted to you could factor out<BR>\n" );
document.write( "the 11 that is common to both terms to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11%2A%281+%2B+x%2Asqrt%282%29%29 ALIGN=MIDDLE  ALT=\"11%2A%281+%2B+x%2Asqrt%282%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > but that's up to you<BR>\n" );
document.write( "and what your instructions are.<BR>\n" );
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document.write( "Hope this helps you to understand the problem a little more. </SPAN>\n" );
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