document.write( "Question 59007: what number is larger: sq rt of 7 + sq rt of 10 or sq rt of 3 + sq rt of 19?\r
\n" ); document.write( "\n" ); document.write( "I just dont undertand this problem. I know you are supposed to factor if number is not a perfect sqaure but these are prime numbers. help me please!! \n" ); document.write( "
Algebra.Com's Answer #40505 by stanbon(75887)\"\" \"About 
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what number is larger: sq rt of 7 + sq rt of 10 or sq rt of 3 + sq rt of 19?
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\n" ); document.write( "Since we don't know how they are related we'll use \"R\" instead of =,>, or <.
\n" ); document.write( "sqrt7+sqrt10 R sqrt3+sqrt19
\n" ); document.write( "Square both sides to get:
\n" ); document.write( "17+2sqrt(70) R 22+sqrt(57)
\n" ); document.write( "2sqrt70 R 5+sqrt57
\n" ); document.write( "sqrt70 - sqrt57 R (5/2)
\n" ); document.write( "Square again to get:
\n" ); document.write( "13-2sqrt(70*57) R 25/4
\n" ); document.write( "27/4 R 2sqrt(3990)
\n" ); document.write( "27/8 R sqrt(3990)
\n" ); document.write( "Square again to get:
\n" ); document.write( "729/64 R 3990
\n" ); document.write( "Now we see that R is <
\n" ); document.write( "So sqrt7+sqrt10 is less than sqrt3 + sqrt19
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\n" ); document.write( "Using a calculator you get
\n" ); document.write( "The left side is 5.8080...
\n" ); document.write( "The right side is 6.0909...
\n" ); document.write( "So we were right: R is <
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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