Simplify Square Root of 51310

What is the square root of 51310 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.

√51310 = A√B

Unfortunately, the square root of 51310 cannot be simplified. Thus, here is the answer to the square root of 51310 in its simplest form:

√ 51310 = √ 51310

Here are two different methods we used to determine why the square root of 51310 cannot be simplified.

1) To be able to simplify the square root of 51310, one of the factors of 51310 other than 1 must be a perfect square. The factors of 51310 are 1, 2, 5, 7, 10, 14, 35, 70, 733, 1466, 3665, 5131, 7330, 10262, 25655, and 51310. Since none of these factors are perfect squares, the square root of 51310 cannot be simplified.

2) To be able to simplify the square root of 51310, all the prime factors of 51310 cannot be unique. When we did prime factorization of 51310, we found that 2 x 5 x 7 x 733 equals 51310. Since all the prime factors are unique, the square root of 51310 cannot be simplified.

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