Simplify Square Root of 12374

What is the square root of 12374 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.

√12374 = A√B

Unfortunately, the square root of 12374 cannot be simplified. Thus, here is the answer to the square root of 12374 in its simplest form:

√ 12374 = √ 12374

Here are two different methods we used to determine why the square root of 12374 cannot be simplified.

1) To be able to simplify the square root of 12374, one of the factors of 12374 other than 1 must be a perfect square. The factors of 12374 are 1, 2, 23, 46, 269, 538, 6187, and 12374. Since none of these factors are perfect squares, the square root of 12374 cannot be simplified.

2) To be able to simplify the square root of 12374, all the prime factors of 12374 cannot be unique. When we did prime factorization of 12374, we found that 2 x 23 x 269 equals 12374. Since all the prime factors are unique, the square root of 12374 cannot be simplified.

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