Simplify Square Root of 8459

What is the square root of 8459 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.

√8459 = A√B

Unfortunately, the square root of 8459 cannot be simplified. Thus, here is the answer to the square root of 8459 in its simplest form:

√ 8459 = √ 8459

Here are two different methods we used to determine why the square root of 8459 cannot be simplified.

1) To be able to simplify the square root of 8459, one of the factors of 8459 other than 1 must be a perfect square. The factors of 8459 are 1, 11, 769, and 8459. Since none of these factors are perfect squares, the square root of 8459 cannot be simplified.

2) To be able to simplify the square root of 8459, all the prime factors of 8459 cannot be unique. When we did prime factorization of 8459, we found that 11 x 769 equals 8459. Since all the prime factors are unique, the square root of 8459 cannot be simplified.

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