Simplify Square Root of 21

What is the square root of 21 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.

√21 = A√B

Unfortunately, the square root of 21 cannot be simplified. Thus, here is the answer to the square root of 21 in its simplest form:

√ 21 = √ 21

Here are two different methods we used to determine why the square root of 21 cannot be simplified.

1) To be able to simplify the square root of 21, one of the factors of 21 other than 1 must be a perfect square. The factors of 21 are 1, 3, 7, and 21. Since none of these factors are perfect squares, the square root of 21 cannot be simplified.

2) To be able to simplify the square root of 21, all the prime factors of 21 cannot be unique. When we did prime factorization of 21, we found that 3 x 7 equals 21. Since all the prime factors are unique, the square root of 21 cannot be simplified.

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