Simplify Square Root of 81374

What is the square root of 81374 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.

√81374 = A√B

Unfortunately, the square root of 81374 cannot be simplified. Thus, here is the answer to the square root of 81374 in its simplest form:

√ 81374 = √ 81374

Here are two different methods we used to determine why the square root of 81374 cannot be simplified.

1) To be able to simplify the square root of 81374, one of the factors of 81374 other than 1 must be a perfect square. The factors of 81374 are 1, 2, 23, 29, 46, 58, 61, 122, 667, 1334, 1403, 1769, 2806, 3538, 40687, and 81374. Since none of these factors are perfect squares, the square root of 81374 cannot be simplified.

2) To be able to simplify the square root of 81374, all the prime factors of 81374 cannot be unique. When we did prime factorization of 81374, we found that 2 x 23 x 29 x 61 equals 81374. Since all the prime factors are unique, the square root of 81374 cannot be simplified.

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