Simplify Square Root of 25338

What is the square root of 25338 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.

√25338 = A√B

Unfortunately, the square root of 25338 cannot be simplified. Thus, here is the answer to the square root of 25338 in its simplest form:

√ 25338 = √ 25338

Here are two different methods we used to determine why the square root of 25338 cannot be simplified.

1) To be able to simplify the square root of 25338, one of the factors of 25338 other than 1 must be a perfect square. The factors of 25338 are 1, 2, 3, 6, 41, 82, 103, 123, 206, 246, 309, 618, 4223, 8446, 12669, and 25338. Since none of these factors are perfect squares, the square root of 25338 cannot be simplified.

2) To be able to simplify the square root of 25338, all the prime factors of 25338 cannot be unique. When we did prime factorization of 25338, we found that 2 x 3 x 41 x 103 equals 25338. Since all the prime factors are unique, the square root of 25338 cannot be simplified.

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