Simplify Square Root of 21257

What is the square root of 21257 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.

√21257 = A√B

Unfortunately, the square root of 21257 cannot be simplified. Thus, here is the answer to the square root of 21257 in its simplest form:

√ 21257 = √ 21257

Here are two different methods we used to determine why the square root of 21257 cannot be simplified.

1) To be able to simplify the square root of 21257, one of the factors of 21257 other than 1 must be a perfect square. The factors of 21257 are 1, 29, 733, and 21257. Since none of these factors are perfect squares, the square root of 21257 cannot be simplified.

2) To be able to simplify the square root of 21257, all the prime factors of 21257 cannot be unique. When we did prime factorization of 21257, we found that 29 x 733 equals 21257. Since all the prime factors are unique, the square root of 21257 cannot be simplified.

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