Simplify Square Root of 81467

What is the square root of 81467 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.

√81467 = A√B

Unfortunately, the square root of 81467 cannot be simplified. Thus, here is the answer to the square root of 81467 in its simplest form:

√ 81467 = √ 81467

Here are two different methods we used to determine why the square root of 81467 cannot be simplified.

1) To be able to simplify the square root of 81467, one of the factors of 81467 other than 1 must be a perfect square. The factors of 81467 are 1, 41, 1987, and 81467. Since none of these factors are perfect squares, the square root of 81467 cannot be simplified.

2) To be able to simplify the square root of 81467, all the prime factors of 81467 cannot be unique. When we did prime factorization of 81467, we found that 41 x 1987 equals 81467. Since all the prime factors are unique, the square root of 81467 cannot be simplified.

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