Simplify Square Root of 21293

What is the square root of 21293 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.

√21293 = A√B

Unfortunately, the square root of 21293 cannot be simplified. Thus, here is the answer to the square root of 21293 in its simplest form:

√ 21293 = √ 21293

Here are two different methods we used to determine why the square root of 21293 cannot be simplified.

1) To be able to simplify the square root of 21293, one of the factors of 21293 other than 1 must be a perfect square. The factors of 21293 are 1, 107, 199, and 21293. Since none of these factors are perfect squares, the square root of 21293 cannot be simplified.

2) To be able to simplify the square root of 21293, all the prime factors of 21293 cannot be unique. When we did prime factorization of 21293, we found that 107 x 199 equals 21293. Since all the prime factors are unique, the square root of 21293 cannot be simplified.

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