Simplify Square Root of 21946

What is the square root of 21946 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.

√21946 = A√B

Unfortunately, the square root of 21946 cannot be simplified. Thus, here is the answer to the square root of 21946 in its simplest form:

√ 21946 = √ 21946

Here are two different methods we used to determine why the square root of 21946 cannot be simplified.

1) To be able to simplify the square root of 21946, one of the factors of 21946 other than 1 must be a perfect square. The factors of 21946 are 1, 2, 10973, and 21946. Since none of these factors are perfect squares, the square root of 21946 cannot be simplified.

2) To be able to simplify the square root of 21946, all the prime factors of 21946 cannot be unique. When we did prime factorization of 21946, we found that 2 x 10973 equals 21946. Since all the prime factors are unique, the square root of 21946 cannot be simplified.

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