document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209214>Question 1209214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The radical <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%2880%29%2Bsqrt%281776%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28%2880%29%2Bsqrt%281776%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be expressed as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28a%29+%2Bsqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%28a%29+%2Bsqrt%28b%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where a < b. What is the product \"ab\"? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847846 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=847846\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>444</font>\r<BR>\n" );
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document.write( "Explanation<BR>\n" );
document.write( "I'll assume that a,b are positive integers.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2880%2Bsqrt%281776%29%29=sqrt%28a%29+%2Bsqrt%28b%29 ALIGN=MIDDLE  ALT=\"sqrt%2880%2Bsqrt%281776%29%29=sqrt%28a%29+%2Bsqrt%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%2880%2Bsqrt%281776%29%29%29%5E2=%28sqrt%28a%29+%2Bsqrt%28b%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%2880%2Bsqrt%281776%29%29%29%5E2=%28sqrt%28a%29+%2Bsqrt%28b%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=80%2Bsqrt%281776%29=%28sqrt%28a%29%29%5E2%2B2%2Asqrt%28a%29%2Asqrt%28b%29%2B%28sqrt%28b%29%29%5E2 ALIGN=MIDDLE   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=80%2Bsqrt%281776%29=a%2B2%2Asqrt%28ab%29%2Bb ALIGN=MIDDLE  ALT=\"80%2Bsqrt%281776%29=a%2B2%2Asqrt%28ab%29%2Bb\"   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=80%2Bsqrt%281776%29=%28a%2Bb%29%2B2%2Asqrt%28ab%29 ALIGN=MIDDLE  ALT=\"80%2Bsqrt%281776%29=%28a%2Bb%29%2B2%2Asqrt%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=highlight%2880%29%2Bhighlight_green%28sqrt%281776%29%29=highlight%28a%2Bb%29%2Bhighlight_green%282%2Asqrt%28ab%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Notice these matching pairs on either side\r<BR>\n" );
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document.write( "The red and green boxes indicate that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb+=+80 ALIGN=MIDDLE  ALT=\"a%2Bb+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Asqrt%28ab%29+=+sqrt%281776%29 ALIGN=MIDDLE  ALT=\"2%2Asqrt%28ab%29+=+sqrt%281776%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Rewrite the 2nd equation like so<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2Asqrt%28ab%29%29%5E2+=+%28sqrt%281776%29%29%5E2 ALIGN=MIDDLE  ALT=\"%282%2Asqrt%28ab%29%29%5E2+=+%28sqrt%281776%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=4ab+=+1776 ALIGN=MIDDLE  ALT=\"4ab+=+1776\"   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+=+1776%2F4 ALIGN=MIDDLE  ALT=\"ab+=+1776%2F4\"   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+=+444 ALIGN=MIDDLE  ALT=\"ab+=+444\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Extra info:<BR>\n" );
document.write( "Solving the system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28a%2Bb+=+80%2C+2%2Asqrt%28ab%29+=+sqrt%281776%29%29 ALIGN=MIDDLE  ALT=\"system%28a%2Bb+=+80%2C+2%2Asqrt%28ab%29+=+sqrt%281776%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > leads to (a,b) = (6,74) when considering a < b <BR>\n" );
document.write( "a+b = 6+74 = 80<BR>\n" );
document.write( "a*b = 6*74 = <font color=red>444</font><BR>\n" );
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