Simplify Square Root of 4254

What is the square root of 4254 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.

√4254 = A√B

Unfortunately, the square root of 4254 cannot be simplified. Thus, here is the answer to the square root of 4254 in its simplest form:

√ 4254 = √ 4254

Here are two different methods we used to determine why the square root of 4254 cannot be simplified.

1) To be able to simplify the square root of 4254, one of the factors of 4254 other than 1 must be a perfect square. The factors of 4254 are 1, 2, 3, 6, 709, 1418, 2127, and 4254. Since none of these factors are perfect squares, the square root of 4254 cannot be simplified.

2) To be able to simplify the square root of 4254, all the prime factors of 4254 cannot be unique. When we did prime factorization of 4254, we found that 2 x 3 x 709 equals 4254. Since all the prime factors are unique, the square root of 4254 cannot be simplified.

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