Simplify Square Root of 21619

What is the square root of 21619 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.

√21619 = A√B

Unfortunately, the square root of 21619 cannot be simplified. Thus, here is the answer to the square root of 21619 in its simplest form:

√ 21619 = √ 21619

Here are two different methods we used to determine why the square root of 21619 cannot be simplified.

1) To be able to simplify the square root of 21619, one of the factors of 21619 other than 1 must be a perfect square. The factors of 21619 are 1, 13, 1663, and 21619. Since none of these factors are perfect squares, the square root of 21619 cannot be simplified.

2) To be able to simplify the square root of 21619, all the prime factors of 21619 cannot be unique. When we did prime factorization of 21619, we found that 13 x 1663 equals 21619. Since all the prime factors are unique, the square root of 21619 cannot be simplified.

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