Simplify Square Root of 51563

What is the square root of 51563 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.

√51563 = A√B

Unfortunately, the square root of 51563 cannot be simplified. Thus, here is the answer to the square root of 51563 in its simplest form:

√ 51563 = √ 51563

Here are two different methods we used to determine why the square root of 51563 cannot be simplified.

1) To be able to simplify the square root of 51563, one of the factors of 51563 other than 1 must be a perfect square. The factors of 51563 are 1 and 51563. Since none of these factors are perfect squares, the square root of 51563 cannot be simplified.

2) To be able to simplify the square root of 51563, all the prime factors of 51563 cannot be unique. When we did prime factorization of 51563, we found that 51563 equals 51563. Since all the prime factors are unique, the square root of 51563 cannot be simplified.

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