Simplify Square Root of 21694

What is the square root of 21694 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.

√21694 = A√B

Unfortunately, the square root of 21694 cannot be simplified. Thus, here is the answer to the square root of 21694 in its simplest form:

√ 21694 = √ 21694

Here are two different methods we used to determine why the square root of 21694 cannot be simplified.

1) To be able to simplify the square root of 21694, one of the factors of 21694 other than 1 must be a perfect square. The factors of 21694 are 1, 2, 10847, and 21694. Since none of these factors are perfect squares, the square root of 21694 cannot be simplified.

2) To be able to simplify the square root of 21694, all the prime factors of 21694 cannot be unique. When we did prime factorization of 21694, we found that 2 x 10847 equals 21694. Since all the prime factors are unique, the square root of 21694 cannot be simplified.

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