Simplify Square Root of 78677

What is the square root of 78677 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.

√78677 = A√B

Unfortunately, the square root of 78677 cannot be simplified. Thus, here is the answer to the square root of 78677 in its simplest form:

√ 78677 = √ 78677

Here are two different methods we used to determine why the square root of 78677 cannot be simplified.

1) To be able to simplify the square root of 78677, one of the factors of 78677 other than 1 must be a perfect square. The factors of 78677 are 1, 29, 2713, and 78677. Since none of these factors are perfect squares, the square root of 78677 cannot be simplified.

2) To be able to simplify the square root of 78677, all the prime factors of 78677 cannot be unique. When we did prime factorization of 78677, we found that 29 x 2713 equals 78677. Since all the prime factors are unique, the square root of 78677 cannot be simplified.

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