Simplify Square Root of 76785

What is the square root of 76785 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.

√76785 = A√B

Unfortunately, the square root of 76785 cannot be simplified. Thus, here is the answer to the square root of 76785 in its simplest form:

√ 76785 = √ 76785

Here are two different methods we used to determine why the square root of 76785 cannot be simplified.

1) To be able to simplify the square root of 76785, one of the factors of 76785 other than 1 must be a perfect square. The factors of 76785 are 1, 3, 5, 15, 5119, 15357, 25595, and 76785. Since none of these factors are perfect squares, the square root of 76785 cannot be simplified.

2) To be able to simplify the square root of 76785, all the prime factors of 76785 cannot be unique. When we did prime factorization of 76785, we found that 3 x 5 x 5119 equals 76785. Since all the prime factors are unique, the square root of 76785 cannot be simplified.

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