Simplify Square Root of 55257

What is the square root of 55257 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.

√55257 = A√B

Unfortunately, the square root of 55257 cannot be simplified. Thus, here is the answer to the square root of 55257 in its simplest form:

√ 55257 = √ 55257

Here are two different methods we used to determine why the square root of 55257 cannot be simplified.

1) To be able to simplify the square root of 55257, one of the factors of 55257 other than 1 must be a perfect square. The factors of 55257 are 1, 3, 113, 163, 339, 489, 18419, and 55257. Since none of these factors are perfect squares, the square root of 55257 cannot be simplified.

2) To be able to simplify the square root of 55257, all the prime factors of 55257 cannot be unique. When we did prime factorization of 55257, we found that 3 x 113 x 163 equals 55257. Since all the prime factors are unique, the square root of 55257 cannot be simplified.

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