Simplify Square Root of 3

What is the square root of 3 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.

√3 = A√B

Unfortunately, the square root of 3 cannot be simplified. Thus, here is the answer to the square root of 3 in its simplest form:

√ 3 = √ 3

Here are two different methods we used to determine why the square root of 3 cannot be simplified.

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

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

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