Simplify Square Root of 6757

What is the square root of 6757 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.

√6757 = A√B

Unfortunately, the square root of 6757 cannot be simplified. Thus, here is the answer to the square root of 6757 in its simplest form:

√ 6757 = √ 6757

Here are two different methods we used to determine why the square root of 6757 cannot be simplified.

1) To be able to simplify the square root of 6757, one of the factors of 6757 other than 1 must be a perfect square. The factors of 6757 are 1, 29, 233, and 6757. Since none of these factors are perfect squares, the square root of 6757 cannot be simplified.

2) To be able to simplify the square root of 6757, all the prime factors of 6757 cannot be unique. When we did prime factorization of 6757, we found that 29 x 233 equals 6757. Since all the prime factors are unique, the square root of 6757 cannot be simplified.

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