Simplify Square Root of 43674

What is the square root of 43674 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.

√43674 = A√B

Unfortunately, the square root of 43674 cannot be simplified. Thus, here is the answer to the square root of 43674 in its simplest form:

√ 43674 = √ 43674

Here are two different methods we used to determine why the square root of 43674 cannot be simplified.

1) To be able to simplify the square root of 43674, one of the factors of 43674 other than 1 must be a perfect square. The factors of 43674 are 1, 2, 3, 6, 29, 58, 87, 174, 251, 502, 753, 1506, 7279, 14558, 21837, and 43674. Since none of these factors are perfect squares, the square root of 43674 cannot be simplified.

2) To be able to simplify the square root of 43674, all the prime factors of 43674 cannot be unique. When we did prime factorization of 43674, we found that 2 x 3 x 29 x 251 equals 43674. Since all the prime factors are unique, the square root of 43674 cannot be simplified.

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