Simplify Square Root of 255

What is the square root of 255 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.

√255 = A√B

Unfortunately, the square root of 255 cannot be simplified. Thus, here is the answer to the square root of 255 in its simplest form:

√ 255 = √ 255

Here are two different methods we used to determine why the square root of 255 cannot be simplified.

1) To be able to simplify the square root of 255, one of the factors of 255 other than 1 must be a perfect square. The factors of 255 are 1, 3, 5, 15, 17, 51, 85, and 255. Since none of these factors are perfect squares, the square root of 255 cannot be simplified.

2) To be able to simplify the square root of 255, all the prime factors of 255 cannot be unique. When we did prime factorization of 255, we found that 3 x 5 x 17 equals 255. Since all the prime factors are unique, the square root of 255 cannot be simplified.

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Simplify Square Root of 256
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