Simplify Square Root of 21270

What is the square root of 21270 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.

√21270 = A√B

Unfortunately, the square root of 21270 cannot be simplified. Thus, here is the answer to the square root of 21270 in its simplest form:

√ 21270 = √ 21270

Here are two different methods we used to determine why the square root of 21270 cannot be simplified.

1) To be able to simplify the square root of 21270, one of the factors of 21270 other than 1 must be a perfect square. The factors of 21270 are 1, 2, 3, 5, 6, 10, 15, 30, 709, 1418, 2127, 3545, 4254, 7090, 10635, and 21270. Since none of these factors are perfect squares, the square root of 21270 cannot be simplified.

2) To be able to simplify the square root of 21270, all the prime factors of 21270 cannot be unique. When we did prime factorization of 21270, we found that 2 x 3 x 5 x 709 equals 21270. Since all the prime factors are unique, the square root of 21270 cannot be simplified.

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