Simplify Square Root of 22361

What is the square root of 22361 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.

√22361 = A√B

Unfortunately, the square root of 22361 cannot be simplified. Thus, here is the answer to the square root of 22361 in its simplest form:

√ 22361 = √ 22361

Here are two different methods we used to determine why the square root of 22361 cannot be simplified.

1) To be able to simplify the square root of 22361, one of the factors of 22361 other than 1 must be a perfect square. The factors of 22361 are 1, 59, 379, and 22361. Since none of these factors are perfect squares, the square root of 22361 cannot be simplified.

2) To be able to simplify the square root of 22361, all the prime factors of 22361 cannot be unique. When we did prime factorization of 22361, we found that 59 x 379 equals 22361. Since all the prime factors are unique, the square root of 22361 cannot be simplified.

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