Simplify Square Root of 43702

What is the square root of 43702 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.

√43702 = A√B

Unfortunately, the square root of 43702 cannot be simplified. Thus, here is the answer to the square root of 43702 in its simplest form:

√ 43702 = √ 43702

Here are two different methods we used to determine why the square root of 43702 cannot be simplified.

1) To be able to simplify the square root of 43702, one of the factors of 43702 other than 1 must be a perfect square. The factors of 43702 are 1, 2, 21851, and 43702. Since none of these factors are perfect squares, the square root of 43702 cannot be simplified.

2) To be able to simplify the square root of 43702, all the prime factors of 43702 cannot be unique. When we did prime factorization of 43702, we found that 2 x 21851 equals 43702. Since all the prime factors are unique, the square root of 43702 cannot be simplified.

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