Simplify Square Root of 14597

What is the square root of 14597 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.

√14597 = A√B

Unfortunately, the square root of 14597 cannot be simplified. Thus, here is the answer to the square root of 14597 in its simplest form:

√ 14597 = √ 14597

Here are two different methods we used to determine why the square root of 14597 cannot be simplified.

1) To be able to simplify the square root of 14597, one of the factors of 14597 other than 1 must be a perfect square. The factors of 14597 are 1, 11, 1327, and 14597. Since none of these factors are perfect squares, the square root of 14597 cannot be simplified.

2) To be able to simplify the square root of 14597, all the prime factors of 14597 cannot be unique. When we did prime factorization of 14597, we found that 11 x 1327 equals 14597. Since all the prime factors are unique, the square root of 14597 cannot be simplified.

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