Simplify Square Root of 11517

What is the square root of 11517 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.

√11517 = A√B

Unfortunately, the square root of 11517 cannot be simplified. Thus, here is the answer to the square root of 11517 in its simplest form:

√ 11517 = √ 11517

Here are two different methods we used to determine why the square root of 11517 cannot be simplified.

1) To be able to simplify the square root of 11517, one of the factors of 11517 other than 1 must be a perfect square. The factors of 11517 are 1, 3, 11, 33, 349, 1047, 3839, and 11517. Since none of these factors are perfect squares, the square root of 11517 cannot be simplified.

2) To be able to simplify the square root of 11517, all the prime factors of 11517 cannot be unique. When we did prime factorization of 11517, we found that 3 x 11 x 349 equals 11517. Since all the prime factors are unique, the square root of 11517 cannot be simplified.

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