SOLUTION: 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?

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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?
Answer by jsmallt9(3296) About Me  (Show Source):
You can put this solution on YOUR website!
The short way to say your problem: Simplify sqrt%2884%29 and then say what number ends up in front of the square root.

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.

4 is a perfect square and it is a factor of 84 so:
sqrt%2884%29+=+sqrt%284%2A21%29+=+sqrt%284%29%2Asqrt%2821%29+=+2sqrt%2821%29
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.

Since sqrt%2884%29 simplifies to 2sqrt%2821%29, the answer to the problem is: 2.