Simplify Square Root of 12307

What is the square root of 12307 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.

√12307 = A√B

Unfortunately, the square root of 12307 cannot be simplified. Thus, here is the answer to the square root of 12307 in its simplest form:

√ 12307 = √ 12307

Here are two different methods we used to determine why the square root of 12307 cannot be simplified.

1) To be able to simplify the square root of 12307, one of the factors of 12307 other than 1 must be a perfect square. The factors of 12307 are 1, 31, 397, and 12307. Since none of these factors are perfect squares, the square root of 12307 cannot be simplified.

2) To be able to simplify the square root of 12307, all the prime factors of 12307 cannot be unique. When we did prime factorization of 12307, we found that 31 x 397 equals 12307. Since all the prime factors are unique, the square root of 12307 cannot be simplified.

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