Simplify Square Root of 72771

What is the square root of 72771 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.

√72771 = A√B

Unfortunately, the square root of 72771 cannot be simplified. Thus, here is the answer to the square root of 72771 in its simplest form:

√ 72771 = √ 72771

Here are two different methods we used to determine why the square root of 72771 cannot be simplified.

1) To be able to simplify the square root of 72771, one of the factors of 72771 other than 1 must be a perfect square. The factors of 72771 are 1, 3, 127, 191, 381, 573, 24257, and 72771. Since none of these factors are perfect squares, the square root of 72771 cannot be simplified.

2) To be able to simplify the square root of 72771, all the prime factors of 72771 cannot be unique. When we did prime factorization of 72771, we found that 3 x 127 x 191 equals 72771. Since all the prime factors are unique, the square root of 72771 cannot be simplified.

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