Simplify Square Root of 63407

What is the square root of 63407 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.

√63407 = A√B

Unfortunately, the square root of 63407 cannot be simplified. Thus, here is the answer to the square root of 63407 in its simplest form:

√ 63407 = √ 63407

Here are two different methods we used to determine why the square root of 63407 cannot be simplified.

1) To be able to simplify the square root of 63407, one of the factors of 63407 other than 1 must be a perfect square. The factors of 63407 are 1, 163, 389, and 63407. Since none of these factors are perfect squares, the square root of 63407 cannot be simplified.

2) To be able to simplify the square root of 63407, all the prime factors of 63407 cannot be unique. When we did prime factorization of 63407, we found that 163 x 389 equals 63407. Since all the prime factors are unique, the square root of 63407 cannot be simplified.

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