Simplify Square Root of 3309

What is the square root of 3309 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.

√3309 = A√B

Unfortunately, the square root of 3309 cannot be simplified. Thus, here is the answer to the square root of 3309 in its simplest form:

√ 3309 = √ 3309

Here are two different methods we used to determine why the square root of 3309 cannot be simplified.

1) To be able to simplify the square root of 3309, one of the factors of 3309 other than 1 must be a perfect square. The factors of 3309 are 1, 3, 1103, and 3309. Since none of these factors are perfect squares, the square root of 3309 cannot be simplified.

2) To be able to simplify the square root of 3309, all the prime factors of 3309 cannot be unique. When we did prime factorization of 3309, we found that 3 x 1103 equals 3309. Since all the prime factors are unique, the square root of 3309 cannot be simplified.

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