Simplify Square Root of 2

What is the square root of 2 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.

√2 = A√B

Unfortunately, the square root of 2 cannot be simplified. Thus, here is the answer to the square root of 2 in its simplest form:

√ 2 = √ 2

Here are two different methods we used to determine why the square root of 2 cannot be simplified.

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

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

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