Simplify Square Root of 6861

What is the square root of 6861 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.

√6861 = A√B

Unfortunately, the square root of 6861 cannot be simplified. Thus, here is the answer to the square root of 6861 in its simplest form:

√ 6861 = √ 6861

Here are two different methods we used to determine why the square root of 6861 cannot be simplified.

1) To be able to simplify the square root of 6861, one of the factors of 6861 other than 1 must be a perfect square. The factors of 6861 are 1, 3, 2287, and 6861. Since none of these factors are perfect squares, the square root of 6861 cannot be simplified.

2) To be able to simplify the square root of 6861, all the prime factors of 6861 cannot be unique. When we did prime factorization of 6861, we found that 3 x 2287 equals 6861. Since all the prime factors are unique, the square root of 6861 cannot be simplified.

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