Simplify Square Root of 80983

What is the square root of 80983 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.

√80983 = A√B

Unfortunately, the square root of 80983 cannot be simplified. Thus, here is the answer to the square root of 80983 in its simplest form:

√ 80983 = √ 80983

Here are two different methods we used to determine why the square root of 80983 cannot be simplified.

1) To be able to simplify the square root of 80983, one of the factors of 80983 other than 1 must be a perfect square. The factors of 80983 are 1, 7, 23, 161, 503, 3521, 11569, and 80983. Since none of these factors are perfect squares, the square root of 80983 cannot be simplified.

2) To be able to simplify the square root of 80983, all the prime factors of 80983 cannot be unique. When we did prime factorization of 80983, we found that 7 x 23 x 503 equals 80983. Since all the prime factors are unique, the square root of 80983 cannot be simplified.

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