Simplify Square Root of 63253

What is the square root of 63253 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.

√63253 = A√B

Unfortunately, the square root of 63253 cannot be simplified. Thus, here is the answer to the square root of 63253 in its simplest form:

√ 63253 = √ 63253

Here are two different methods we used to determine why the square root of 63253 cannot be simplified.

1) To be able to simplify the square root of 63253, one of the factors of 63253 other than 1 must be a perfect square. The factors of 63253 are 1, 43, 1471, and 63253. Since none of these factors are perfect squares, the square root of 63253 cannot be simplified.

2) To be able to simplify the square root of 63253, all the prime factors of 63253 cannot be unique. When we did prime factorization of 63253, we found that 43 x 1471 equals 63253. Since all the prime factors are unique, the square root of 63253 cannot be simplified.

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