Simplify Square Root of 54134

What is the square root of 54134 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.

√54134 = A√B

Unfortunately, the square root of 54134 cannot be simplified. Thus, here is the answer to the square root of 54134 in its simplest form:

√ 54134 = √ 54134

Here are two different methods we used to determine why the square root of 54134 cannot be simplified.

1) To be able to simplify the square root of 54134, one of the factors of 54134 other than 1 must be a perfect square. The factors of 54134 are 1, 2, 27067, and 54134. Since none of these factors are perfect squares, the square root of 54134 cannot be simplified.

2) To be able to simplify the square root of 54134, all the prime factors of 54134 cannot be unique. When we did prime factorization of 54134, we found that 2 x 27067 equals 54134. Since all the prime factors are unique, the square root of 54134 cannot be simplified.

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