Simplify Square Root of 24537

What is the square root of 24537 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.

√24537 = A√B

Unfortunately, the square root of 24537 cannot be simplified. Thus, here is the answer to the square root of 24537 in its simplest form:

√ 24537 = √ 24537

Here are two different methods we used to determine why the square root of 24537 cannot be simplified.

1) To be able to simplify the square root of 24537, one of the factors of 24537 other than 1 must be a perfect square. The factors of 24537 are 1, 3, 8179, and 24537. Since none of these factors are perfect squares, the square root of 24537 cannot be simplified.

2) To be able to simplify the square root of 24537, all the prime factors of 24537 cannot be unique. When we did prime factorization of 24537, we found that 3 x 8179 equals 24537. Since all the prime factors are unique, the square root of 24537 cannot be simplified.

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