Simplify Square Root of 54354

What is the square root of 54354 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.

√54354 = A√B

Unfortunately, the square root of 54354 cannot be simplified. Thus, here is the answer to the square root of 54354 in its simplest form:

√ 54354 = √ 54354

Here are two different methods we used to determine why the square root of 54354 cannot be simplified.

1) To be able to simplify the square root of 54354, one of the factors of 54354 other than 1 must be a perfect square. The factors of 54354 are 1, 2, 3, 6, 9059, 18118, 27177, and 54354. Since none of these factors are perfect squares, the square root of 54354 cannot be simplified.

2) To be able to simplify the square root of 54354, all the prime factors of 54354 cannot be unique. When we did prime factorization of 54354, we found that 2 x 3 x 9059 equals 54354. Since all the prime factors are unique, the square root of 54354 cannot be simplified.

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