Simplify Square Root of 591

What is the square root of 591 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.

√591 = A√B

Unfortunately, the square root of 591 cannot be simplified. Thus, here is the answer to the square root of 591 in its simplest form:

√ 591 = √ 591

Here are two different methods we used to determine why the square root of 591 cannot be simplified.

1) To be able to simplify the square root of 591, one of the factors of 591 other than 1 must be a perfect square. The factors of 591 are 1, 3, 197, and 591. Since none of these factors are perfect squares, the square root of 591 cannot be simplified.

2) To be able to simplify the square root of 591, all the prime factors of 591 cannot be unique. When we did prime factorization of 591, we found that 3 x 197 equals 591. Since all the prime factors are unique, the square root of 591 cannot be simplified.

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