Simplify Square Root of 52054

What is the square root of 52054 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.

√52054 = A√B

Unfortunately, the square root of 52054 cannot be simplified. Thus, here is the answer to the square root of 52054 in its simplest form:

√ 52054 = √ 52054

Here are two different methods we used to determine why the square root of 52054 cannot be simplified.

1) To be able to simplify the square root of 52054, one of the factors of 52054 other than 1 must be a perfect square. The factors of 52054 are 1, 2, 17, 34, 1531, 3062, 26027, and 52054. Since none of these factors are perfect squares, the square root of 52054 cannot be simplified.

2) To be able to simplify the square root of 52054, all the prime factors of 52054 cannot be unique. When we did prime factorization of 52054, we found that 2 x 17 x 1531 equals 52054. Since all the prime factors are unique, the square root of 52054 cannot be simplified.

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