Simplify Square Root of 12667

What is the square root of 12667 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.

√12667 = A√B

Unfortunately, the square root of 12667 cannot be simplified. Thus, here is the answer to the square root of 12667 in its simplest form:

√ 12667 = √ 12667

Here are two different methods we used to determine why the square root of 12667 cannot be simplified.

1) To be able to simplify the square root of 12667, one of the factors of 12667 other than 1 must be a perfect square. The factors of 12667 are 1, 53, 239, and 12667. Since none of these factors are perfect squares, the square root of 12667 cannot be simplified.

2) To be able to simplify the square root of 12667, all the prime factors of 12667 cannot be unique. When we did prime factorization of 12667, we found that 53 x 239 equals 12667. Since all the prime factors are unique, the square root of 12667 cannot be simplified.

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