Simplify Square Root of 51130

What is the square root of 51130 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.

√51130 = A√B

Unfortunately, the square root of 51130 cannot be simplified. Thus, here is the answer to the square root of 51130 in its simplest form:

√ 51130 = √ 51130

Here are two different methods we used to determine why the square root of 51130 cannot be simplified.

1) To be able to simplify the square root of 51130, one of the factors of 51130 other than 1 must be a perfect square. The factors of 51130 are 1, 2, 5, 10, 5113, 10226, 25565, and 51130. Since none of these factors are perfect squares, the square root of 51130 cannot be simplified.

2) To be able to simplify the square root of 51130, all the prime factors of 51130 cannot be unique. When we did prime factorization of 51130, we found that 2 x 5 x 5113 equals 51130. Since all the prime factors are unique, the square root of 51130 cannot be simplified.

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