Simplify Square Root of 33007

What is the square root of 33007 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.

√33007 = A√B

Unfortunately, the square root of 33007 cannot be simplified. Thus, here is the answer to the square root of 33007 in its simplest form:

√ 33007 = √ 33007

Here are two different methods we used to determine why the square root of 33007 cannot be simplified.

1) To be able to simplify the square root of 33007, one of the factors of 33007 other than 1 must be a perfect square. The factors of 33007 are 1, 13, 2539, and 33007. Since none of these factors are perfect squares, the square root of 33007 cannot be simplified.

2) To be able to simplify the square root of 33007, all the prime factors of 33007 cannot be unique. When we did prime factorization of 33007, we found that 13 x 2539 equals 33007. Since all the prime factors are unique, the square root of 33007 cannot be simplified.

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