Simplify Square Root of 63302

What is the square root of 63302 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.

√63302 = A√B

Unfortunately, the square root of 63302 cannot be simplified. Thus, here is the answer to the square root of 63302 in its simplest form:

√ 63302 = √ 63302

Here are two different methods we used to determine why the square root of 63302 cannot be simplified.

1) To be able to simplify the square root of 63302, one of the factors of 63302 other than 1 must be a perfect square. The factors of 63302 are 1, 2, 31, 62, 1021, 2042, 31651, and 63302. Since none of these factors are perfect squares, the square root of 63302 cannot be simplified.

2) To be able to simplify the square root of 63302, all the prime factors of 63302 cannot be unique. When we did prime factorization of 63302, we found that 2 x 31 x 1021 equals 63302. Since all the prime factors are unique, the square root of 63302 cannot be simplified.

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