Simplify Square Root of 12382

What is the square root of 12382 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.

√12382 = A√B

Unfortunately, the square root of 12382 cannot be simplified. Thus, here is the answer to the square root of 12382 in its simplest form:

√ 12382 = √ 12382

Here are two different methods we used to determine why the square root of 12382 cannot be simplified.

1) To be able to simplify the square root of 12382, one of the factors of 12382 other than 1 must be a perfect square. The factors of 12382 are 1, 2, 41, 82, 151, 302, 6191, and 12382. Since none of these factors are perfect squares, the square root of 12382 cannot be simplified.

2) To be able to simplify the square root of 12382, all the prime factors of 12382 cannot be unique. When we did prime factorization of 12382, we found that 2 x 41 x 151 equals 12382. Since all the prime factors are unique, the square root of 12382 cannot be simplified.

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