Simplify Square Root of 39355

What is the square root of 39355 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.

√39355 = A√B

Unfortunately, the square root of 39355 cannot be simplified. Thus, here is the answer to the square root of 39355 in its simplest form:

√ 39355 = √ 39355

Here are two different methods we used to determine why the square root of 39355 cannot be simplified.

1) To be able to simplify the square root of 39355, one of the factors of 39355 other than 1 must be a perfect square. The factors of 39355 are 1, 5, 17, 85, 463, 2315, 7871, and 39355. Since none of these factors are perfect squares, the square root of 39355 cannot be simplified.

2) To be able to simplify the square root of 39355, all the prime factors of 39355 cannot be unique. When we did prime factorization of 39355, we found that 5 x 17 x 463 equals 39355. Since all the prime factors are unique, the square root of 39355 cannot be simplified.

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