Simplify Square Root of 27966

What is the square root of 27966 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.

√27966 = A√B

Unfortunately, the square root of 27966 cannot be simplified. Thus, here is the answer to the square root of 27966 in its simplest form:

√ 27966 = √ 27966

Here are two different methods we used to determine why the square root of 27966 cannot be simplified.

1) To be able to simplify the square root of 27966, one of the factors of 27966 other than 1 must be a perfect square. The factors of 27966 are 1, 2, 3, 6, 59, 79, 118, 158, 177, 237, 354, 474, 4661, 9322, 13983, and 27966. Since none of these factors are perfect squares, the square root of 27966 cannot be simplified.

2) To be able to simplify the square root of 27966, all the prime factors of 27966 cannot be unique. When we did prime factorization of 27966, we found that 2 x 3 x 59 x 79 equals 27966. Since all the prime factors are unique, the square root of 27966 cannot be simplified.

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