Simplify Square Root of 76935

What is the square root of 76935 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.

√76935 = A√B

Unfortunately, the square root of 76935 cannot be simplified. Thus, here is the answer to the square root of 76935 in its simplest form:

√ 76935 = √ 76935

Here are two different methods we used to determine why the square root of 76935 cannot be simplified.

1) To be able to simplify the square root of 76935, one of the factors of 76935 other than 1 must be a perfect square. The factors of 76935 are 1, 3, 5, 15, 23, 69, 115, 223, 345, 669, 1115, 3345, 5129, 15387, 25645, and 76935. Since none of these factors are perfect squares, the square root of 76935 cannot be simplified.

2) To be able to simplify the square root of 76935, all the prime factors of 76935 cannot be unique. When we did prime factorization of 76935, we found that 3 x 5 x 23 x 223 equals 76935. Since all the prime factors are unique, the square root of 76935 cannot be simplified.

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