Simplify Square Root of 27642

What is the square root of 27642 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.

√27642 = A√B

Unfortunately, the square root of 27642 cannot be simplified. Thus, here is the answer to the square root of 27642 in its simplest form:

√ 27642 = √ 27642

Here are two different methods we used to determine why the square root of 27642 cannot be simplified.

1) To be able to simplify the square root of 27642, one of the factors of 27642 other than 1 must be a perfect square. The factors of 27642 are 1, 2, 3, 6, 17, 34, 51, 102, 271, 542, 813, 1626, 4607, 9214, 13821, and 27642. Since none of these factors are perfect squares, the square root of 27642 cannot be simplified.

2) To be able to simplify the square root of 27642, all the prime factors of 27642 cannot be unique. When we did prime factorization of 27642, we found that 2 x 3 x 17 x 271 equals 27642. Since all the prime factors are unique, the square root of 27642 cannot be simplified.

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