document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1171178>Question 1171178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The radical √(85+√2736) can be expressed as √a + √b, where a < b. What is the product of ab?\r<BR>\n" );
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document.write( "(I know I'm supposed to solve this using a^2 + 2ab + b^2 = (a+b)^2, but have no idea as to how to implement it. Any advice/tips/help would be greatly appreciated) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #796098 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=796098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2885%2Bsqrt%282736%29%29+=+sqrt%28a%29+%2B+sqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%2885%2Bsqrt%282736%29%29+=+sqrt%28a%29+%2B+sqrt%28b%29\"   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=%28sqrt%2885%2Bsqrt%282736%29%29%29%5E2+=+%28sqrt%28a%29+%2B+sqrt%28b%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%2885%2Bsqrt%282736%29%29%29%5E2+=+%28sqrt%28a%29+%2B+sqrt%28b%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Squaring both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85%2Bsqrt%282736%29+=+a+%2B+2sqrt%28ab%29%2B+b ALIGN=MIDDLE  ALT=\"85%2Bsqrt%282736%29+=+a+%2B+2sqrt%28ab%29%2B+b\"   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=85%2Bsqrt%284%2A684%29+=+%28a%2Bb%29+%2B+2sqrt%28ab%29 ALIGN=MIDDLE  ALT=\"85%2Bsqrt%284%2A684%29+=+%28a%2Bb%29+%2B+2sqrt%28ab%29\"   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=85%2Bsqrt%284%29%2Asqrt%28684%29+=+%28a%2Bb%29+%2B+2sqrt%28ab%29 ALIGN=MIDDLE  ALT=\"85%2Bsqrt%284%29%2Asqrt%28684%29+=+%28a%2Bb%29+%2B+2sqrt%28ab%29\"   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=85%2B2%2Asqrt%28684%29+=+%28a%2Bb%29+%2B+2sqrt%28ab%29 ALIGN=MIDDLE  ALT=\"85%2B2%2Asqrt%28684%29+=+%28a%2Bb%29+%2B+2sqrt%28ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We see that the first pair of terms leads to a+b = 85, but we won't need this fact. \r<BR>\n" );
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document.write( "Equating the second pair of terms leads to<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28684%29+=+sqrt%28ab%29 ALIGN=MIDDLE  ALT=\"sqrt%28684%29+=+sqrt%28ab%29\"   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=%28sqrt%28684%29%29%5E2+=+%28sqrt%28ab%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28684%29%29%5E2+=+%28sqrt%28ab%29%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=684+=+ab ALIGN=MIDDLE  ALT=\"684+=+ab\"   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=ab+=+684 ALIGN=MIDDLE  ALT=\"ab+=+684\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is the final answer.\r<BR>\n" );
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document.write( "Side note: You could use a+b = 85 and ab = 684 as a system of equations to solve for 'a' and b to find that a = 9 and b = 76; however, this isn't needed if you just want to find ab. <BR>\n" );
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