document.write( "Question 674933: How do you solve and simplify square roots? For example the square root of 117 \n" ); document.write( "

Algebra.Com's Answer #419475 by DrBeeee(684) $\"\"$ $\"About$

You can put this solution on YOUR website!
First of all, the number of which you are trying to get the square root must contain at least one perfect square as a factor. Secondly, you can not \"simplify\" the square root of a prime number. You want
\n" ); document.write( "(1) x = $\"sqrt%28117%29\"$
\n" ); document.write( "So we must be able to factor 117
\n" ); document.write( "(2) 117 = 3*39 or
\n" ); document.write( "(3) 117 = 3*3*13 or
\n" ); document.write( "(4) 117 = (3^2)*(13)
\n" ); document.write( "Then (1) becomes
\n" ); document.write( "(5) x = $\"sqrt%28%283%5E2%29%2A%2813%29%29\"$
\n" ); document.write( "Now use the very useful identity
\n" ); document.write( "(6) $\"sqrt%28a%2Ab%29\"$ = $\"sqrt%28a%29\"$ * $\"sqrt%28b%29\"$
\n" ); document.write( "Then (5) becomes your answer
\n" ); document.write( "(7) x = 3* $\"sqrt%2813%29\"$ \n" ); document.write( "

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