Simplify Square Root of 76558

What is the square root of 76558 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.

√76558 = A√B

Unfortunately, the square root of 76558 cannot be simplified. Thus, here is the answer to the square root of 76558 in its simplest form:

√ 76558 = √ 76558

Here are two different methods we used to determine why the square root of 76558 cannot be simplified.

1) To be able to simplify the square root of 76558, one of the factors of 76558 other than 1 must be a perfect square. The factors of 76558 are 1, 2, 101, 202, 379, 758, 38279, and 76558. Since none of these factors are perfect squares, the square root of 76558 cannot be simplified.

2) To be able to simplify the square root of 76558, all the prime factors of 76558 cannot be unique. When we did prime factorization of 76558, we found that 2 x 101 x 379 equals 76558. Since all the prime factors are unique, the square root of 76558 cannot be simplified.

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