Simplify Square Root of 218

What is the square root of 218 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.

√218 = A√B

Unfortunately, the square root of 218 cannot be simplified. Thus, here is the answer to the square root of 218 in its simplest form:

√ 218 = √ 218

Here are two different methods we used to determine why the square root of 218 cannot be simplified.

1) To be able to simplify the square root of 218, one of the factors of 218 other than 1 must be a perfect square. The factors of 218 are 1, 2, 109, and 218. Since none of these factors are perfect squares, the square root of 218 cannot be simplified.

2) To be able to simplify the square root of 218, all the prime factors of 218 cannot be unique. When we did prime factorization of 218, we found that 2 x 109 equals 218. Since all the prime factors are unique, the square root of 218 cannot be simplified.

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