document.write( "Question 280781: if the square root of 84 is simplified to a x the square root of b such that a and b are integers, what is the value of a? \n" ); document.write( "

Algebra.Com's Answer #204436 by jsmallt9(3758) $\"\"$ $\"About$

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The short way to say your problem: Simplify $\"sqrt%2884%29\"$ and then say what number ends up in front of the square root.

\n" ); document.write( "Simplifying square roots involves factoring out perfect square factors, if any, and rationalizing denominators. $\"sqrt%2884%29\"$ has no denominators so do not be concerned with rationalizing. All we have to do is see if 84 has any perfect square factors.

\n" ); document.write( "4 is a perfect square and it is a factor of 84 so:
\n" ); document.write( " $\"sqrt%2884%29+=+sqrt%284%2A21%29+=+sqrt%284%29%2Asqrt%2821%29+=+2sqrt%2821%29\"$
\n" ); document.write( "Like reducing fractions, you keep simplifying square roots until you can go no further. 21 has no perfect square factors so we cannot simplify any further.

\n" ); document.write( "Since $\"sqrt%2884%29\"$ simplifies to $\"2sqrt%2821%29\"$ , the answer to the problem is: 2. \n" ); document.write( "

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