Simplify Square Root of 86666

What is the square root of 86666 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.

√86666 = A√B

Unfortunately, the square root of 86666 cannot be simplified. Thus, here is the answer to the square root of 86666 in its simplest form:

√ 86666 = √ 86666

Here are two different methods we used to determine why the square root of 86666 cannot be simplified.

1) To be able to simplify the square root of 86666, one of the factors of 86666 other than 1 must be a perfect square. The factors of 86666 are 1, 2, 17, 34, 2549, 5098, 43333, and 86666. Since none of these factors are perfect squares, the square root of 86666 cannot be simplified.

2) To be able to simplify the square root of 86666, all the prime factors of 86666 cannot be unique. When we did prime factorization of 86666, we found that 2 x 17 x 2549 equals 86666. Since all the prime factors are unique, the square root of 86666 cannot be simplified.

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