Simplify Square Root of 21622

What is the square root of 21622 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.

√21622 = A√B

Unfortunately, the square root of 21622 cannot be simplified. Thus, here is the answer to the square root of 21622 in its simplest form:

√ 21622 = √ 21622

Here are two different methods we used to determine why the square root of 21622 cannot be simplified.

1) To be able to simplify the square root of 21622, one of the factors of 21622 other than 1 must be a perfect square. The factors of 21622 are 1, 2, 19, 38, 569, 1138, 10811, and 21622. Since none of these factors are perfect squares, the square root of 21622 cannot be simplified.

2) To be able to simplify the square root of 21622, all the prime factors of 21622 cannot be unique. When we did prime factorization of 21622, we found that 2 x 19 x 569 equals 21622. Since all the prime factors are unique, the square root of 21622 cannot be simplified.

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