Simplify Square Root of 53111

What is the square root of 53111 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.

√53111 = A√B

Unfortunately, the square root of 53111 cannot be simplified. Thus, here is the answer to the square root of 53111 in its simplest form:

√ 53111 = √ 53111

Here are two different methods we used to determine why the square root of 53111 cannot be simplified.

1) To be able to simplify the square root of 53111, one of the factors of 53111 other than 1 must be a perfect square. The factors of 53111 are 1, 173, 307, and 53111. Since none of these factors are perfect squares, the square root of 53111 cannot be simplified.

2) To be able to simplify the square root of 53111, all the prime factors of 53111 cannot be unique. When we did prime factorization of 53111, we found that 173 x 307 equals 53111. Since all the prime factors are unique, the square root of 53111 cannot be simplified.

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