Simplify Square Root of 12607

What is the square root of 12607 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.

√12607 = A√B

Unfortunately, the square root of 12607 cannot be simplified. Thus, here is the answer to the square root of 12607 in its simplest form:

√ 12607 = √ 12607

Here are two different methods we used to determine why the square root of 12607 cannot be simplified.

1) To be able to simplify the square root of 12607, one of the factors of 12607 other than 1 must be a perfect square. The factors of 12607 are 1, 7, 1801, and 12607. Since none of these factors are perfect squares, the square root of 12607 cannot be simplified.

2) To be able to simplify the square root of 12607, all the prime factors of 12607 cannot be unique. When we did prime factorization of 12607, we found that 7 x 1801 equals 12607. Since all the prime factors are unique, the square root of 12607 cannot be simplified.

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