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?

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(3758) (Show Source): You can put this solution on YOUR website!
The short way to say your problem: Simplify 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. 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:

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 simplifies to , the answer to the problem is: 2.
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