Simplify Square Root of 52602

What is the square root of 52602 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.

√52602 = A√B

Unfortunately, the square root of 52602 cannot be simplified. Thus, here is the answer to the square root of 52602 in its simplest form:

√ 52602 = √ 52602

Here are two different methods we used to determine why the square root of 52602 cannot be simplified.

1) To be able to simplify the square root of 52602, one of the factors of 52602 other than 1 must be a perfect square. The factors of 52602 are 1, 2, 3, 6, 11, 22, 33, 66, 797, 1594, 2391, 4782, 8767, 17534, 26301, and 52602. Since none of these factors are perfect squares, the square root of 52602 cannot be simplified.

2) To be able to simplify the square root of 52602, all the prime factors of 52602 cannot be unique. When we did prime factorization of 52602, we found that 2 x 3 x 11 x 797 equals 52602. Since all the prime factors are unique, the square root of 52602 cannot be simplified.

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