Simplify Square Root of 59501

What is the square root of 59501 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.

√59501 = A√B

Unfortunately, the square root of 59501 cannot be simplified. Thus, here is the answer to the square root of 59501 in its simplest form:

√ 59501 = √ 59501

Here are two different methods we used to determine why the square root of 59501 cannot be simplified.

1) To be able to simplify the square root of 59501, one of the factors of 59501 other than 1 must be a perfect square. The factors of 59501 are 1, 13, 23, 199, 299, 2587, 4577, and 59501. Since none of these factors are perfect squares, the square root of 59501 cannot be simplified.

2) To be able to simplify the square root of 59501, all the prime factors of 59501 cannot be unique. When we did prime factorization of 59501, we found that 13 x 23 x 199 equals 59501. Since all the prime factors are unique, the square root of 59501 cannot be simplified.

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