Simplify Square Root of 33333

What is the square root of 33333 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.

√33333 = A√B

Unfortunately, the square root of 33333 cannot be simplified. Thus, here is the answer to the square root of 33333 in its simplest form:

√ 33333 = √ 33333

Here are two different methods we used to determine why the square root of 33333 cannot be simplified.

1) To be able to simplify the square root of 33333, one of the factors of 33333 other than 1 must be a perfect square. The factors of 33333 are 1, 3, 41, 123, 271, 813, 11111, and 33333. Since none of these factors are perfect squares, the square root of 33333 cannot be simplified.

2) To be able to simplify the square root of 33333, all the prime factors of 33333 cannot be unique. When we did prime factorization of 33333, we found that 3 x 41 x 271 equals 33333. Since all the prime factors are unique, the square root of 33333 cannot be simplified.

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