Simplify Square Root of 56822

What is the square root of 56822 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.

√56822 = A√B

Unfortunately, the square root of 56822 cannot be simplified. Thus, here is the answer to the square root of 56822 in its simplest form:

√ 56822 = √ 56822

Here are two different methods we used to determine why the square root of 56822 cannot be simplified.

1) To be able to simplify the square root of 56822, one of the factors of 56822 other than 1 must be a perfect square. The factors of 56822 are 1, 2, 28411, and 56822. Since none of these factors are perfect squares, the square root of 56822 cannot be simplified.

2) To be able to simplify the square root of 56822, all the prime factors of 56822 cannot be unique. When we did prime factorization of 56822, we found that 2 x 28411 equals 56822. Since all the prime factors are unique, the square root of 56822 cannot be simplified.

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