Simplify Square Root of 11991

What is the square root of 11991 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.

√11991 = A√B

Unfortunately, the square root of 11991 cannot be simplified. Thus, here is the answer to the square root of 11991 in its simplest form:

√ 11991 = √ 11991

Here are two different methods we used to determine why the square root of 11991 cannot be simplified.

1) To be able to simplify the square root of 11991, one of the factors of 11991 other than 1 must be a perfect square. The factors of 11991 are 1, 3, 7, 21, 571, 1713, 3997, and 11991. Since none of these factors are perfect squares, the square root of 11991 cannot be simplified.

2) To be able to simplify the square root of 11991, all the prime factors of 11991 cannot be unique. When we did prime factorization of 11991, we found that 3 x 7 x 571 equals 11991. Since all the prime factors are unique, the square root of 11991 cannot be simplified.

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