Simplify Square Root of 34134

What is the square root of 34134 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.

√34134 = A√B

Unfortunately, the square root of 34134 cannot be simplified. Thus, here is the answer to the square root of 34134 in its simplest form:

√ 34134 = √ 34134

Here are two different methods we used to determine why the square root of 34134 cannot be simplified.

1) To be able to simplify the square root of 34134, one of the factors of 34134 other than 1 must be a perfect square. The factors of 34134 are 1, 2, 3, 6, 5689, 11378, 17067, and 34134. Since none of these factors are perfect squares, the square root of 34134 cannot be simplified.

2) To be able to simplify the square root of 34134, all the prime factors of 34134 cannot be unique. When we did prime factorization of 34134, we found that 2 x 3 x 5689 equals 34134. Since all the prime factors are unique, the square root of 34134 cannot be simplified.

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