Simplify Square Root of 51510

What is the square root of 51510 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.

√51510 = A√B

Unfortunately, the square root of 51510 cannot be simplified. Thus, here is the answer to the square root of 51510 in its simplest form:

√ 51510 = √ 51510

Here are two different methods we used to determine why the square root of 51510 cannot be simplified.

1) To be able to simplify the square root of 51510, one of the factors of 51510 other than 1 must be a perfect square. The factors of 51510 are 1, 2, 3, 5, 6, 10, 15, 17, 30, 34, 51, 85, 101, 102, 170, 202, 255, 303, 505, 510, 606, 1010, 1515, 1717, 3030, 3434, 5151, 8585, 10302, 17170, 25755, and 51510. Since none of these factors are perfect squares, the square root of 51510 cannot be simplified.

2) To be able to simplify the square root of 51510, all the prime factors of 51510 cannot be unique. When we did prime factorization of 51510, we found that 2 x 3 x 5 x 17 x 101 equals 51510. Since all the prime factors are unique, the square root of 51510 cannot be simplified.

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