Simplify Square Root of 96114

What is the square root of 96114 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.

√96114 = A√B

Unfortunately, the square root of 96114 cannot be simplified. Thus, here is the answer to the square root of 96114 in its simplest form:

√ 96114 = √ 96114

Here are two different methods we used to determine why the square root of 96114 cannot be simplified.

1) To be able to simplify the square root of 96114, one of the factors of 96114 other than 1 must be a perfect square. The factors of 96114 are 1, 2, 3, 6, 83, 166, 193, 249, 386, 498, 579, 1158, 16019, 32038, 48057, and 96114. Since none of these factors are perfect squares, the square root of 96114 cannot be simplified.

2) To be able to simplify the square root of 96114, all the prime factors of 96114 cannot be unique. When we did prime factorization of 96114, we found that 2 x 3 x 83 x 193 equals 96114. Since all the prime factors are unique, the square root of 96114 cannot be simplified.

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