Simplify Square Root of 54998

What is the square root of 54998 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.

√54998 = A√B

Unfortunately, the square root of 54998 cannot be simplified. Thus, here is the answer to the square root of 54998 in its simplest form:

√ 54998 = √ 54998

Here are two different methods we used to determine why the square root of 54998 cannot be simplified.

1) To be able to simplify the square root of 54998, one of the factors of 54998 other than 1 must be a perfect square. The factors of 54998 are 1, 2, 107, 214, 257, 514, 27499, and 54998. Since none of these factors are perfect squares, the square root of 54998 cannot be simplified.

2) To be able to simplify the square root of 54998, all the prime factors of 54998 cannot be unique. When we did prime factorization of 54998, we found that 2 x 107 x 257 equals 54998. Since all the prime factors are unique, the square root of 54998 cannot be simplified.

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