Simplify Square Root of 6

What is the square root of 6 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.

√6 = A√B

Unfortunately, the square root of 6 cannot be simplified. Thus, here is the answer to the square root of 6 in its simplest form:

√ 6 = √ 6

Here are two different methods we used to determine why the square root of 6 cannot be simplified.

1) To be able to simplify the square root of 6, one of the factors of 6 other than 1 must be a perfect square. The factors of 6 are 1, 2, 3, and 6. Since none of these factors are perfect squares, the square root of 6 cannot be simplified.

2) To be able to simplify the square root of 6, all the prime factors of 6 cannot be unique. When we did prime factorization of 6, we found that 2 x 3 equals 6. Since all the prime factors are unique, the square root of 6 cannot be simplified.

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