document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209554>Question 1209554</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Simplify<BR>\n" );
document.write( "(89 + 28√10)^(¼) = √a + √b </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849418 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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/cgi-bin/show-face.mpl?user=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849418\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Consider this general case:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%28a%29%2Bsqrt%28b%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28sqrt%28a%29%2Bsqrt%28b%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B2sqrt%28ab%29%2Bb ALIGN=MIDDLE  ALT=\"a%2B2sqrt%28ab%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28a%2Bb%29%2B2sqrt%28ab%29 ALIGN=MIDDLE  ALT=\"%28a%2Bb%29%2B2sqrt%28ab%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Turning that operation around, if we need to evaluate<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28p%2B2sqrt%28q%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28p%2B2sqrt%28q%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "then the requirement is to find a and b such that p = a+b and q = ab.<br><BR>\n" );
document.write( "Example 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%2B2sqrt%2815%29%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2B2sqrt%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a+b=8; ab=15 --> a and b are 3 and 5 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%288%2B2sqrt%2815%29%29=sqrt%283%29%2Bsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%288%2B2sqrt%2815%29%29=sqrt%283%29%2Bsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Example 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B4sqrt%2815%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B4sqrt%2815%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B2sqrt%2860%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B2sqrt%2860%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a+b=16; ab=60 --> a and b are 6 and 10 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2816%2B4sqrt%2815%29%29=sqrt%286%29%2Bsqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2816%2B4sqrt%2815%29%29=sqrt%286%29%2Bsqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now for your problem....<br><BR>\n" );
document.write( "We are to find the 4th root of the given expression, so we will use the process described above to find the square root of the given expression and use the process again to find the 4th root.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2889%2B28sqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2889%2B28sqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2889%2B2sqrt%28%2814%5E2%29%2810%29%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2889%2B2sqrt%28%2814%5E2%29%2810%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2889%2B2sqrt%281960%29%29 ALIGN=MIDDLE  ALT=\"sqrt%2889%2B2sqrt%281960%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a+b=89; ab=1960 --> a and b are 40 and 49 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2889%2B28sqrt%2810%29%29=sqrt%2840%29%2Bsqrt%2849%29=7%2B2sqrt%2810%29 ALIGN=MIDDLE  ALT=\"sqrt%2889%2B28sqrt%2810%29%29=sqrt%2840%29%2Bsqrt%2849%29=7%2B2sqrt%2810%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%2B2sqrt%2810%29%29 ALIGN=MIDDLE  ALT=\"sqrt%287%2B2sqrt%2810%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a+b=7; ab=10 --> a and b are 2 and 5 --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%287%2B2sqrt%2810%29%29=sqrt%282%29%2Bsqrt%285%29 ALIGN=MIDDLE  ALT=\"sqrt%287%2B2sqrt%2810%29%29=sqrt%282%29%2Bsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%284%2C89%2B28sqrt%2810%29%29=sqrt%287%2B2sqrt%2810%29%29=sqrt%282%29%2Bsqrt%285%29 ALIGN=MIDDLE  ALT=\"root%284%2C89%2B28sqrt%2810%29%29=sqrt%287%2B2sqrt%2810%29%29=sqrt%282%29%2Bsqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );