Simplify Square Root of 40339

What is the square root of 40339 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.

√40339 = A√B

Unfortunately, the square root of 40339 cannot be simplified. Thus, here is the answer to the square root of 40339 in its simplest form:

√ 40339 = √ 40339

Here are two different methods we used to determine why the square root of 40339 cannot be simplified.

1) To be able to simplify the square root of 40339, one of the factors of 40339 other than 1 must be a perfect square. The factors of 40339 are 1, 13, 29, 107, 377, 1391, 3103, and 40339. Since none of these factors are perfect squares, the square root of 40339 cannot be simplified.

2) To be able to simplify the square root of 40339, all the prime factors of 40339 cannot be unique. When we did prime factorization of 40339, we found that 13 x 29 x 107 equals 40339. Since all the prime factors are unique, the square root of 40339 cannot be simplified.

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