Simplify Square Root of 65427

What is the square root of 65427 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.

√65427 = A√B

Unfortunately, the square root of 65427 cannot be simplified. Thus, here is the answer to the square root of 65427 in its simplest form:

√ 65427 = √ 65427

Here are two different methods we used to determine why the square root of 65427 cannot be simplified.

1) To be able to simplify the square root of 65427, one of the factors of 65427 other than 1 must be a perfect square. The factors of 65427 are 1, 3, 113, 193, 339, 579, 21809, and 65427. Since none of these factors are perfect squares, the square root of 65427 cannot be simplified.

2) To be able to simplify the square root of 65427, all the prime factors of 65427 cannot be unique. When we did prime factorization of 65427, we found that 3 x 113 x 193 equals 65427. Since all the prime factors are unique, the square root of 65427 cannot be simplified.

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