Simplify Square Root of 33357

What is the square root of 33357 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.

√33357 = A√B

Unfortunately, the square root of 33357 cannot be simplified. Thus, here is the answer to the square root of 33357 in its simplest form:

√ 33357 = √ 33357

Here are two different methods we used to determine why the square root of 33357 cannot be simplified.

1) To be able to simplify the square root of 33357, one of the factors of 33357 other than 1 must be a perfect square. The factors of 33357 are 1, 3, 11119, and 33357. Since none of these factors are perfect squares, the square root of 33357 cannot be simplified.

2) To be able to simplify the square root of 33357, all the prime factors of 33357 cannot be unique. When we did prime factorization of 33357, we found that 3 x 11119 equals 33357. Since all the prime factors are unique, the square root of 33357 cannot be simplified.

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