Simplify Square Root of 11647

What is the square root of 11647 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.

√11647 = A√B

Unfortunately, the square root of 11647 cannot be simplified. Thus, here is the answer to the square root of 11647 in its simplest form:

√ 11647 = √ 11647

Here are two different methods we used to determine why the square root of 11647 cannot be simplified.

1) To be able to simplify the square root of 11647, one of the factors of 11647 other than 1 must be a perfect square. The factors of 11647 are 1, 19, 613, and 11647. Since none of these factors are perfect squares, the square root of 11647 cannot be simplified.

2) To be able to simplify the square root of 11647, all the prime factors of 11647 cannot be unique. When we did prime factorization of 11647, we found that 19 x 613 equals 11647. Since all the prime factors are unique, the square root of 11647 cannot be simplified.

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