Simplify Square Root of 83627

What is the square root of 83627 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.

√83627 = A√B

Unfortunately, the square root of 83627 cannot be simplified. Thus, here is the answer to the square root of 83627 in its simplest form:

√ 83627 = √ 83627

Here are two different methods we used to determine why the square root of 83627 cannot be simplified.

1) To be able to simplify the square root of 83627, one of the factors of 83627 other than 1 must be a perfect square. The factors of 83627 are 1, 241, 347, and 83627. Since none of these factors are perfect squares, the square root of 83627 cannot be simplified.

2) To be able to simplify the square root of 83627, all the prime factors of 83627 cannot be unique. When we did prime factorization of 83627, we found that 241 x 347 equals 83627. Since all the prime factors are unique, the square root of 83627 cannot be simplified.

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