Simplify Square Root of 52499

What is the square root of 52499 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.

√52499 = A√B

Unfortunately, the square root of 52499 cannot be simplified. Thus, here is the answer to the square root of 52499 in its simplest form:

√ 52499 = √ 52499

Here are two different methods we used to determine why the square root of 52499 cannot be simplified.

1) To be able to simplify the square root of 52499, one of the factors of 52499 other than 1 must be a perfect square. The factors of 52499 are 1, 47, 1117, and 52499. Since none of these factors are perfect squares, the square root of 52499 cannot be simplified.

2) To be able to simplify the square root of 52499, all the prime factors of 52499 cannot be unique. When we did prime factorization of 52499, we found that 47 x 1117 equals 52499. Since all the prime factors are unique, the square root of 52499 cannot be simplified.

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