Simplify Square Root of 10857

What is the square root of 10857 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.

√10857 = A√B

Unfortunately, the square root of 10857 cannot be simplified. Thus, here is the answer to the square root of 10857 in its simplest form:

√ 10857 = √ 10857

Here are two different methods we used to determine why the square root of 10857 cannot be simplified.

1) To be able to simplify the square root of 10857, one of the factors of 10857 other than 1 must be a perfect square. The factors of 10857 are 1, 3, 7, 11, 21, 33, 47, 77, 141, 231, 329, 517, 987, 1551, 3619, and 10857. Since none of these factors are perfect squares, the square root of 10857 cannot be simplified.

2) To be able to simplify the square root of 10857, all the prime factors of 10857 cannot be unique. When we did prime factorization of 10857, we found that 3 x 7 x 11 x 47 equals 10857. Since all the prime factors are unique, the square root of 10857 cannot be simplified.

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