document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=971212>Question 971212</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Q. If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+sqrt%283%29+%2B+sqrt%285%29 ALIGN=MIDDLE  ALT=\"a+=+sqrt%283%29+%2B+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ; b=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28sqrt%283%29%2Bsqrt%285%29%29 ALIGN=MIDDLE  ALT=\"sqrt%28sqrt%283%29%2Bsqrt%285%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=a%2Fb ALIGN=MIDDLE  ALT=\"r=a%2Fb\"   DISABLED_style= \"max-width:90%; height:auto;\" >, then real no. r satisfies the inequality ______ .<BR>\n" );
document.write( "Options:<BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%29+%3C+r+%3C+2 ALIGN=MIDDLE  ALT=\"sqrt%282%29+%3C+r+%3C+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fsqrt%282%29%29+%3C+r+%3C+sqrt%282%29 ALIGN=MIDDLE  ALT=\"%281%2Fsqrt%282%29%29+%3C+r+%3C+sqrt%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2+%3C+r+%3C+sqrt%285%29 ALIGN=MIDDLE  ALT=\"2+%3C+r+%3C+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "d)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%285%29+%3C+r+%3C+3 ALIGN=MIDDLE  ALT=\"sqrt%285%29+%3C+r+%3C+3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Please give the solution process. The expression is directly given in r. I am unable to write the question in one go, so I used variables 'a' and 'b' for numerator and denominator.\r<BR>\n" );
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document.write( "PS: I have tried rationalizing and got upto <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+sqrt%283%29+%2B+sqrt%285%29 ALIGN=MIDDLE  ALT=\"r%5E2+=+sqrt%283%29+%2B+sqrt%285%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #593773 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=593773\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a = square root(3) + square root(5) = 3.968118785<BR>\n" );
document.write( "b = square root(a) = 1.992013751<BR>\n" );
document.write( "a/b = 3.968118785 / 1.992013751 = 1.992013751<BR>\n" );
document.write( "answer is a.<BR>\n" );
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document.write( "alternate solution<BR>\n" );
document.write( "a = square root(3) + square root(5) <BR>\n" );
document.write( "r = a / a^(1/2) = ((a^(1/2)) * (a^(1/2))) / (a^(1/2)) = a^(1/2)<BR>\n" );
document.write( "now substitute for a<BR>\n" );
document.write( "r = (square root(3) + square root(5))^(1/2) = 1.992013751<BR>\n" );
document.write( "answer is a.<BR>\n" );
document.write( " </SPAN>\n" );
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