Simplify Square Root of 22335

What is the square root of 22335 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.

√22335 = A√B

Unfortunately, the square root of 22335 cannot be simplified. Thus, here is the answer to the square root of 22335 in its simplest form:

√ 22335 = √ 22335

Here are two different methods we used to determine why the square root of 22335 cannot be simplified.

1) To be able to simplify the square root of 22335, one of the factors of 22335 other than 1 must be a perfect square. The factors of 22335 are 1, 3, 5, 15, 1489, 4467, 7445, and 22335. Since none of these factors are perfect squares, the square root of 22335 cannot be simplified.

2) To be able to simplify the square root of 22335, all the prime factors of 22335 cannot be unique. When we did prime factorization of 22335, we found that 3 x 5 x 1489 equals 22335. Since all the prime factors are unique, the square root of 22335 cannot be simplified.

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