
What is the square root of 52591 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.
√52591 = A√B
Unfortunately, the square root of 52591 cannot be simplified. Thus, here is the answer to the square root of 52591 in its simplest form:
√ 52591 = √ 52591
Here are two different methods we used to determine why the square root of 52591 cannot be simplified.
1) To be able to simplify the square root of 52591, one of the factors of 52591 other than 1 must be a perfect square. The factors of 52591 are 1, 7, 11, 77, 683, 4781, 7513, and 52591. Since none of these factors are perfect squares, the square root of 52591 cannot be simplified.
2) To be able to simplify the square root of 52591, all the prime factors of 52591 cannot be unique. When we did prime factorization of 52591, we found that 7 x 11 x 683 equals 52591. Since all the prime factors are unique, the square root of 52591 cannot be simplified.
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