Simplify Square Root of 11563

What is the square root of 11563 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.

√11563 = A√B

Unfortunately, the square root of 11563 cannot be simplified. Thus, here is the answer to the square root of 11563 in its simplest form:

√ 11563 = √ 11563

Here are two different methods we used to determine why the square root of 11563 cannot be simplified.

1) To be able to simplify the square root of 11563, one of the factors of 11563 other than 1 must be a perfect square. The factors of 11563 are 1, 31, 373, and 11563. Since none of these factors are perfect squares, the square root of 11563 cannot be simplified.

2) To be able to simplify the square root of 11563, all the prime factors of 11563 cannot be unique. When we did prime factorization of 11563, we found that 31 x 373 equals 11563. Since all the prime factors are unique, the square root of 11563 cannot be simplified.

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