Simplify Square Root of 71966

What is the square root of 71966 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.

√71966 = A√B

Unfortunately, the square root of 71966 cannot be simplified. Thus, here is the answer to the square root of 71966 in its simplest form:

√ 71966 = √ 71966

Here are two different methods we used to determine why the square root of 71966 cannot be simplified.

1) To be able to simplify the square root of 71966, one of the factors of 71966 other than 1 must be a perfect square. The factors of 71966 are 1, 2, 35983, and 71966. Since none of these factors are perfect squares, the square root of 71966 cannot be simplified.

2) To be able to simplify the square root of 71966, all the prime factors of 71966 cannot be unique. When we did prime factorization of 71966, we found that 2 x 35983 equals 71966. Since all the prime factors are unique, the square root of 71966 cannot be simplified.

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