Simplify Square Root of 76678

What is the square root of 76678 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.

√76678 = A√B

Unfortunately, the square root of 76678 cannot be simplified. Thus, here is the answer to the square root of 76678 in its simplest form:

√ 76678 = √ 76678

Here are two different methods we used to determine why the square root of 76678 cannot be simplified.

1) To be able to simplify the square root of 76678, one of the factors of 76678 other than 1 must be a perfect square. The factors of 76678 are 1, 2, 7, 14, 5477, 10954, 38339, and 76678. Since none of these factors are perfect squares, the square root of 76678 cannot be simplified.

2) To be able to simplify the square root of 76678, all the prime factors of 76678 cannot be unique. When we did prime factorization of 76678, we found that 2 x 7 x 5477 equals 76678. Since all the prime factors are unique, the square root of 76678 cannot be simplified.

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