Simplify Square Root of 84154

What is the square root of 84154 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.

√84154 = A√B

Unfortunately, the square root of 84154 cannot be simplified. Thus, here is the answer to the square root of 84154 in its simplest form:

√ 84154 = √ 84154

Here are two different methods we used to determine why the square root of 84154 cannot be simplified.

1) To be able to simplify the square root of 84154, one of the factors of 84154 other than 1 must be a perfect square. The factors of 84154 are 1, 2, 7, 14, 6011, 12022, 42077, and 84154. Since none of these factors are perfect squares, the square root of 84154 cannot be simplified.

2) To be able to simplify the square root of 84154, all the prime factors of 84154 cannot be unique. When we did prime factorization of 84154, we found that 2 x 7 x 6011 equals 84154. Since all the prime factors are unique, the square root of 84154 cannot be simplified.

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