Simplify Square Root of 12021

What is the square root of 12021 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.

√12021 = A√B

Unfortunately, the square root of 12021 cannot be simplified. Thus, here is the answer to the square root of 12021 in its simplest form:

√ 12021 = √ 12021

Here are two different methods we used to determine why the square root of 12021 cannot be simplified.

1) To be able to simplify the square root of 12021, one of the factors of 12021 other than 1 must be a perfect square. The factors of 12021 are 1, 3, 4007, and 12021. Since none of these factors are perfect squares, the square root of 12021 cannot be simplified.

2) To be able to simplify the square root of 12021, all the prime factors of 12021 cannot be unique. When we did prime factorization of 12021, we found that 3 x 4007 equals 12021. Since all the prime factors are unique, the square root of 12021 cannot be simplified.

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