Simplify Square Root of 76237

What is the square root of 76237 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.

√76237 = A√B

Unfortunately, the square root of 76237 cannot be simplified. Thus, here is the answer to the square root of 76237 in its simplest form:

√ 76237 = √ 76237

Here are two different methods we used to determine why the square root of 76237 cannot be simplified.

1) To be able to simplify the square root of 76237, one of the factors of 76237 other than 1 must be a perfect square. The factors of 76237 are 1, 7, 10891, and 76237. Since none of these factors are perfect squares, the square root of 76237 cannot be simplified.

2) To be able to simplify the square root of 76237, all the prime factors of 76237 cannot be unique. When we did prime factorization of 76237, we found that 7 x 10891 equals 76237. Since all the prime factors are unique, the square root of 76237 cannot be simplified.

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