document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=87805>Question 87805</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395977223/algebrahomeworkh>algebra structure and method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I'm supposed to express this in simplest radical form.<BR>\n" );
document.write( "(square root of 2 minus 3)(square root of 2 plus 3)<BR>\n" );
document.write( "I'm not sure how you are supposed to do that or is it in simplest form already? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #63707 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=63707\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29+-+3%29%2A%28sqrt%282%29+%2B+3%29 ALIGN=MIDDLE  ALT=\"%28sqrt%282%29+-+3%29%2A%28sqrt%282%29+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "Note that this product is covered by the rule for the product of the sum and difference<BR>\n" );
document.write( "of two quantities. This rule is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a+-+b%29%2A%28a+%2B+b%29+=+a%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"%28a+-+b%29%2A%28a+%2B+b%29+=+a%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "If you actually do the multiplication of (a - b) times (a + b) you will see why this rule<BR>\n" );
document.write( "is true.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Anyhow, if you let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+sqrt%282%29 ALIGN=MIDDLE  ALT=\"a+=+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+3 ALIGN=MIDDLE  ALT=\"b+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" > then, according to the rule, the product<BR>\n" );
document.write( "will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2+-+b%5E2 ALIGN=MIDDLE  ALT=\"a%5E2+-+b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29%29%5E2+-+%283%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%282%29%29%5E2+-+%283%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "But squaring the square root of 2 results in an answer of 2 and squaring 3 results in 9.<BR>\n" );
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document.write( "So according to the rule, the answer is:<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%282%29-3%29%2A%28sqrt%282%29%2B3%29+=+%28sqrt%282%29%29%5E2+-+%283%29%5E2+=+%282+-+9%29+=+-7 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( "The answer is -7 and notice that the radicals are gone completely.<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );