Simplify Square Root of 15567

What is the square root of 15567 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.

√15567 = A√B

Unfortunately, the square root of 15567 cannot be simplified. Thus, here is the answer to the square root of 15567 in its simplest form:

√ 15567 = √ 15567

Here are two different methods we used to determine why the square root of 15567 cannot be simplified.

1) To be able to simplify the square root of 15567, one of the factors of 15567 other than 1 must be a perfect square. The factors of 15567 are 1, 3, 5189, and 15567. Since none of these factors are perfect squares, the square root of 15567 cannot be simplified.

2) To be able to simplify the square root of 15567, all the prime factors of 15567 cannot be unique. When we did prime factorization of 15567, we found that 3 x 5189 equals 15567. Since all the prime factors are unique, the square root of 15567 cannot be simplified.

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