Simplify Square Root of 76746

What is the square root of 76746 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.

√76746 = A√B

Unfortunately, the square root of 76746 cannot be simplified. Thus, here is the answer to the square root of 76746 in its simplest form:

√ 76746 = √ 76746

Here are two different methods we used to determine why the square root of 76746 cannot be simplified.

1) To be able to simplify the square root of 76746, one of the factors of 76746 other than 1 must be a perfect square. The factors of 76746 are 1, 2, 3, 6, 12791, 25582, 38373, and 76746. Since none of these factors are perfect squares, the square root of 76746 cannot be simplified.

2) To be able to simplify the square root of 76746, all the prime factors of 76746 cannot be unique. When we did prime factorization of 76746, we found that 2 x 3 x 12791 equals 76746. Since all the prime factors are unique, the square root of 76746 cannot be simplified.

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