Simplify Square Root of 21210

What is the square root of 21210 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.

√21210 = A√B

Unfortunately, the square root of 21210 cannot be simplified. Thus, here is the answer to the square root of 21210 in its simplest form:

√ 21210 = √ 21210

Here are two different methods we used to determine why the square root of 21210 cannot be simplified.

1) To be able to simplify the square root of 21210, one of the factors of 21210 other than 1 must be a perfect square. The factors of 21210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 101, 105, 202, 210, 303, 505, 606, 707, 1010, 1414, 1515, 2121, 3030, 3535, 4242, 7070, 10605, and 21210. Since none of these factors are perfect squares, the square root of 21210 cannot be simplified.

2) To be able to simplify the square root of 21210, all the prime factors of 21210 cannot be unique. When we did prime factorization of 21210, we found that 2 x 3 x 5 x 7 x 101 equals 21210. Since all the prime factors are unique, the square root of 21210 cannot be simplified.

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