Simplify Square Root of 19921

What is the square root of 19921 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.

√19921 = A√B

Unfortunately, the square root of 19921 cannot be simplified. Thus, here is the answer to the square root of 19921 in its simplest form:

√ 19921 = √ 19921

Here are two different methods we used to determine why the square root of 19921 cannot be simplified.

1) To be able to simplify the square root of 19921, one of the factors of 19921 other than 1 must be a perfect square. The factors of 19921 are 1, 11, 1811, and 19921. Since none of these factors are perfect squares, the square root of 19921 cannot be simplified.

2) To be able to simplify the square root of 19921, all the prime factors of 19921 cannot be unique. When we did prime factorization of 19921, we found that 11 x 1811 equals 19921. Since all the prime factors are unique, the square root of 19921 cannot be simplified.

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