Simplify Square Root of 53414

What is the square root of 53414 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.

√53414 = A√B

Unfortunately, the square root of 53414 cannot be simplified. Thus, here is the answer to the square root of 53414 in its simplest form:

√ 53414 = √ 53414

Here are two different methods we used to determine why the square root of 53414 cannot be simplified.

1) To be able to simplify the square root of 53414, one of the factors of 53414 other than 1 must be a perfect square. The factors of 53414 are 1, 2, 17, 34, 1571, 3142, 26707, and 53414. Since none of these factors are perfect squares, the square root of 53414 cannot be simplified.

2) To be able to simplify the square root of 53414, all the prime factors of 53414 cannot be unique. When we did prime factorization of 53414, we found that 2 x 17 x 1571 equals 53414. Since all the prime factors are unique, the square root of 53414 cannot be simplified.

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