Simplify Square Root of 8439

What is the square root of 8439 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.

√8439 = A√B

Unfortunately, the square root of 8439 cannot be simplified. Thus, here is the answer to the square root of 8439 in its simplest form:

√ 8439 = √ 8439

Here are two different methods we used to determine why the square root of 8439 cannot be simplified.

1) To be able to simplify the square root of 8439, one of the factors of 8439 other than 1 must be a perfect square. The factors of 8439 are 1, 3, 29, 87, 97, 291, 2813, and 8439. Since none of these factors are perfect squares, the square root of 8439 cannot be simplified.

2) To be able to simplify the square root of 8439, all the prime factors of 8439 cannot be unique. When we did prime factorization of 8439, we found that 3 x 29 x 97 equals 8439. Since all the prime factors are unique, the square root of 8439 cannot be simplified.

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