Simplify Square Root of 51702

What is the square root of 51702 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.

√51702 = A√B

Unfortunately, the square root of 51702 cannot be simplified. Thus, here is the answer to the square root of 51702 in its simplest form:

√ 51702 = √ 51702

Here are two different methods we used to determine why the square root of 51702 cannot be simplified.

1) To be able to simplify the square root of 51702, one of the factors of 51702 other than 1 must be a perfect square. The factors of 51702 are 1, 2, 3, 6, 7, 14, 21, 42, 1231, 2462, 3693, 7386, 8617, 17234, 25851, and 51702. Since none of these factors are perfect squares, the square root of 51702 cannot be simplified.

2) To be able to simplify the square root of 51702, all the prime factors of 51702 cannot be unique. When we did prime factorization of 51702, we found that 2 x 3 x 7 x 1231 equals 51702. Since all the prime factors are unique, the square root of 51702 cannot be simplified.

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