Simplify Square Root of 47983

What is the square root of 47983 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.

√47983 = A√B

Unfortunately, the square root of 47983 cannot be simplified. Thus, here is the answer to the square root of 47983 in its simplest form:

√ 47983 = √ 47983

Here are two different methods we used to determine why the square root of 47983 cannot be simplified.

1) To be able to simplify the square root of 47983, one of the factors of 47983 other than 1 must be a perfect square. The factors of 47983 are 1, 13, 3691, and 47983. Since none of these factors are perfect squares, the square root of 47983 cannot be simplified.

2) To be able to simplify the square root of 47983, all the prime factors of 47983 cannot be unique. When we did prime factorization of 47983, we found that 13 x 3691 equals 47983. Since all the prime factors are unique, the square root of 47983 cannot be simplified.

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