Simplify Square Root of 83422

What is the square root of 83422 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√83422 = A√B

Unfortunately, the square root of 83422 cannot be simplified. Thus, here is the answer to the square root of 83422 in its simplest form:

√ 83422 = √ 83422

Here are two different methods we used to determine why the square root of 83422 cannot be simplified.

1) To be able to simplify the square root of 83422, one of the factors of 83422 other than 1 must be a perfect square. The factors of 83422 are 1, 2, 53, 106, 787, 1574, 41711, and 83422. Since none of these factors are perfect squares, the square root of 83422 cannot be simplified.

2) To be able to simplify the square root of 83422, all the prime factors of 83422 cannot be unique. When we did prime factorization of 83422, we found that 2 x 53 x 787 equals 83422. Since all the prime factors are unique, the square root of 83422 cannot be simplified.

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