Simplify Square Root of 83218

What is the square root of 83218 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.

√83218 = A√B

Unfortunately, the square root of 83218 cannot be simplified. Thus, here is the answer to the square root of 83218 in its simplest form:

√ 83218 = √ 83218

Here are two different methods we used to determine why the square root of 83218 cannot be simplified.

1) To be able to simplify the square root of 83218, one of the factors of 83218 other than 1 must be a perfect square. The factors of 83218 are 1, 2, 41609, and 83218. Since none of these factors are perfect squares, the square root of 83218 cannot be simplified.

2) To be able to simplify the square root of 83218, all the prime factors of 83218 cannot be unique. When we did prime factorization of 83218, we found that 2 x 41609 equals 83218. Since all the prime factors are unique, the square root of 83218 cannot be simplified.

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