Simplify Square Root of 59147

What is the square root of 59147 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.

√59147 = A√B

Unfortunately, the square root of 59147 cannot be simplified. Thus, here is the answer to the square root of 59147 in its simplest form:

√ 59147 = √ 59147

Here are two different methods we used to determine why the square root of 59147 cannot be simplified.

1) To be able to simplify the square root of 59147, one of the factors of 59147 other than 1 must be a perfect square. The factors of 59147 are 1, 11, 19, 209, 283, 3113, 5377, and 59147. Since none of these factors are perfect squares, the square root of 59147 cannot be simplified.

2) To be able to simplify the square root of 59147, all the prime factors of 59147 cannot be unique. When we did prime factorization of 59147, we found that 11 x 19 x 283 equals 59147. Since all the prime factors are unique, the square root of 59147 cannot be simplified.

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