Simplify Square Root of 50431

What is the square root of 50431 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.

√50431 = A√B

Unfortunately, the square root of 50431 cannot be simplified. Thus, here is the answer to the square root of 50431 in its simplest form:

√ 50431 = √ 50431

Here are two different methods we used to determine why the square root of 50431 cannot be simplified.

1) To be able to simplify the square root of 50431, one of the factors of 50431 other than 1 must be a perfect square. The factors of 50431 are 1, 29, 37, 47, 1073, 1363, 1739, and 50431. Since none of these factors are perfect squares, the square root of 50431 cannot be simplified.

2) To be able to simplify the square root of 50431, all the prime factors of 50431 cannot be unique. When we did prime factorization of 50431, we found that 29 x 37 x 47 equals 50431. Since all the prime factors are unique, the square root of 50431 cannot be simplified.

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