Simplify Square Root of 7967

What is the square root of 7967 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.

√7967 = A√B

Unfortunately, the square root of 7967 cannot be simplified. Thus, here is the answer to the square root of 7967 in its simplest form:

√ 7967 = √ 7967

Here are two different methods we used to determine why the square root of 7967 cannot be simplified.

1) To be able to simplify the square root of 7967, one of the factors of 7967 other than 1 must be a perfect square. The factors of 7967 are 1, 31, 257, and 7967. Since none of these factors are perfect squares, the square root of 7967 cannot be simplified.

2) To be able to simplify the square root of 7967, all the prime factors of 7967 cannot be unique. When we did prime factorization of 7967, we found that 31 x 257 equals 7967. Since all the prime factors are unique, the square root of 7967 cannot be simplified.

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