Simplify Square Root of 6729

What is the square root of 6729 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.

√6729 = A√B

Unfortunately, the square root of 6729 cannot be simplified. Thus, here is the answer to the square root of 6729 in its simplest form:

√ 6729 = √ 6729

Here are two different methods we used to determine why the square root of 6729 cannot be simplified.

1) To be able to simplify the square root of 6729, one of the factors of 6729 other than 1 must be a perfect square. The factors of 6729 are 1, 3, 2243, and 6729. Since none of these factors are perfect squares, the square root of 6729 cannot be simplified.

2) To be able to simplify the square root of 6729, all the prime factors of 6729 cannot be unique. When we did prime factorization of 6729, we found that 3 x 2243 equals 6729. Since all the prime factors are unique, the square root of 6729 cannot be simplified.

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