Simplify Square Root of 52593

What is the square root of 52593 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.

√52593 = A√B

Unfortunately, the square root of 52593 cannot be simplified. Thus, here is the answer to the square root of 52593 in its simplest form:

√ 52593 = √ 52593

Here are two different methods we used to determine why the square root of 52593 cannot be simplified.

1) To be able to simplify the square root of 52593, one of the factors of 52593 other than 1 must be a perfect square. The factors of 52593 are 1, 3, 47, 141, 373, 1119, 17531, and 52593. Since none of these factors are perfect squares, the square root of 52593 cannot be simplified.

2) To be able to simplify the square root of 52593, all the prime factors of 52593 cannot be unique. When we did prime factorization of 52593, we found that 3 x 47 x 373 equals 52593. Since all the prime factors are unique, the square root of 52593 cannot be simplified.

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