Simplify Square Root of 53770

What is the square root of 53770 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.

√53770 = A√B

Unfortunately, the square root of 53770 cannot be simplified. Thus, here is the answer to the square root of 53770 in its simplest form:

√ 53770 = √ 53770

Here are two different methods we used to determine why the square root of 53770 cannot be simplified.

1) To be able to simplify the square root of 53770, one of the factors of 53770 other than 1 must be a perfect square. The factors of 53770 are 1, 2, 5, 10, 19, 38, 95, 190, 283, 566, 1415, 2830, 5377, 10754, 26885, and 53770. Since none of these factors are perfect squares, the square root of 53770 cannot be simplified.

2) To be able to simplify the square root of 53770, all the prime factors of 53770 cannot be unique. When we did prime factorization of 53770, we found that 2 x 5 x 19 x 283 equals 53770. Since all the prime factors are unique, the square root of 53770 cannot be simplified.

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