Simplify Square Root of 12209

What is the square root of 12209 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.

√12209 = A√B

Unfortunately, the square root of 12209 cannot be simplified. Thus, here is the answer to the square root of 12209 in its simplest form:

√ 12209 = √ 12209

Here are two different methods we used to determine why the square root of 12209 cannot be simplified.

1) To be able to simplify the square root of 12209, one of the factors of 12209 other than 1 must be a perfect square. The factors of 12209 are 1, 29, 421, and 12209. Since none of these factors are perfect squares, the square root of 12209 cannot be simplified.

2) To be able to simplify the square root of 12209, all the prime factors of 12209 cannot be unique. When we did prime factorization of 12209, we found that 29 x 421 equals 12209. Since all the prime factors are unique, the square root of 12209 cannot be simplified.

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