Simplify Square Root of 72794

What is the square root of 72794 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.

√72794 = A√B

Unfortunately, the square root of 72794 cannot be simplified. Thus, here is the answer to the square root of 72794 in its simplest form:

√ 72794 = √ 72794

Here are two different methods we used to determine why the square root of 72794 cannot be simplified.

1) To be able to simplify the square root of 72794, one of the factors of 72794 other than 1 must be a perfect square. The factors of 72794 are 1, 2, 17, 34, 2141, 4282, 36397, and 72794. Since none of these factors are perfect squares, the square root of 72794 cannot be simplified.

2) To be able to simplify the square root of 72794, all the prime factors of 72794 cannot be unique. When we did prime factorization of 72794, we found that 2 x 17 x 2141 equals 72794. Since all the prime factors are unique, the square root of 72794 cannot be simplified.

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