Simplify Square Root of 32334

What is the square root of 32334 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.

√32334 = A√B

Unfortunately, the square root of 32334 cannot be simplified. Thus, here is the answer to the square root of 32334 in its simplest form:

√ 32334 = √ 32334

Here are two different methods we used to determine why the square root of 32334 cannot be simplified.

1) To be able to simplify the square root of 32334, one of the factors of 32334 other than 1 must be a perfect square. The factors of 32334 are 1, 2, 3, 6, 17, 34, 51, 102, 317, 634, 951, 1902, 5389, 10778, 16167, and 32334. Since none of these factors are perfect squares, the square root of 32334 cannot be simplified.

2) To be able to simplify the square root of 32334, all the prime factors of 32334 cannot be unique. When we did prime factorization of 32334, we found that 2 x 3 x 17 x 317 equals 32334. Since all the prime factors are unique, the square root of 32334 cannot be simplified.

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