Simplify Square Root of 499

What is the square root of 499 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.

√499 = A√B

Unfortunately, the square root of 499 cannot be simplified. Thus, here is the answer to the square root of 499 in its simplest form:

√ 499 = √ 499

Here are two different methods we used to determine why the square root of 499 cannot be simplified.

1) To be able to simplify the square root of 499, one of the factors of 499 other than 1 must be a perfect square. The factors of 499 are 1 and 499. Since none of these factors are perfect squares, the square root of 499 cannot be simplified.

2) To be able to simplify the square root of 499, all the prime factors of 499 cannot be unique. When we did prime factorization of 499, we found that 499 equals 499. Since all the prime factors are unique, the square root of 499 cannot be simplified.

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