Simplify Square Root of 8187

What is the square root of 8187 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.

√8187 = A√B

Unfortunately, the square root of 8187 cannot be simplified. Thus, here is the answer to the square root of 8187 in its simplest form:

√ 8187 = √ 8187

Here are two different methods we used to determine why the square root of 8187 cannot be simplified.

1) To be able to simplify the square root of 8187, one of the factors of 8187 other than 1 must be a perfect square. The factors of 8187 are 1, 3, 2729, and 8187. Since none of these factors are perfect squares, the square root of 8187 cannot be simplified.

2) To be able to simplify the square root of 8187, all the prime factors of 8187 cannot be unique. When we did prime factorization of 8187, we found that 3 x 2729 equals 8187. Since all the prime factors are unique, the square root of 8187 cannot be simplified.

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