Simplify Square Root of 53297

What is the square root of 53297 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.

√53297 = A√B

Unfortunately, the square root of 53297 cannot be simplified. Thus, here is the answer to the square root of 53297 in its simplest form:

√ 53297 = √ 53297

Here are two different methods we used to determine why the square root of 53297 cannot be simplified.

1) To be able to simplify the square root of 53297, one of the factors of 53297 other than 1 must be a perfect square. The factors of 53297 are 1, 223, 239, and 53297. Since none of these factors are perfect squares, the square root of 53297 cannot be simplified.

2) To be able to simplify the square root of 53297, all the prime factors of 53297 cannot be unique. When we did prime factorization of 53297, we found that 223 x 239 equals 53297. Since all the prime factors are unique, the square root of 53297 cannot be simplified.

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