Simplify Square Root of 27142

What is the square root of 27142 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.

√27142 = A√B

Unfortunately, the square root of 27142 cannot be simplified. Thus, here is the answer to the square root of 27142 in its simplest form:

√ 27142 = √ 27142

Here are two different methods we used to determine why the square root of 27142 cannot be simplified.

1) To be able to simplify the square root of 27142, one of the factors of 27142 other than 1 must be a perfect square. The factors of 27142 are 1, 2, 41, 82, 331, 662, 13571, and 27142. Since none of these factors are perfect squares, the square root of 27142 cannot be simplified.

2) To be able to simplify the square root of 27142, all the prime factors of 27142 cannot be unique. When we did prime factorization of 27142, we found that 2 x 41 x 331 equals 27142. Since all the prime factors are unique, the square root of 27142 cannot be simplified.

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