Simplify Square Root of 43782

What is the square root of 43782 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.

√43782 = A√B

Unfortunately, the square root of 43782 cannot be simplified. Thus, here is the answer to the square root of 43782 in its simplest form:

√ 43782 = √ 43782

Here are two different methods we used to determine why the square root of 43782 cannot be simplified.

1) To be able to simplify the square root of 43782, one of the factors of 43782 other than 1 must be a perfect square. The factors of 43782 are 1, 2, 3, 6, 7297, 14594, 21891, and 43782. Since none of these factors are perfect squares, the square root of 43782 cannot be simplified.

2) To be able to simplify the square root of 43782, all the prime factors of 43782 cannot be unique. When we did prime factorization of 43782, we found that 2 x 3 x 7297 equals 43782. Since all the prime factors are unique, the square root of 43782 cannot be simplified.

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