Simplify Square Root of 21010

What is the square root of 21010 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.

√21010 = A√B

Unfortunately, the square root of 21010 cannot be simplified. Thus, here is the answer to the square root of 21010 in its simplest form:

√ 21010 = √ 21010

Here are two different methods we used to determine why the square root of 21010 cannot be simplified.

1) To be able to simplify the square root of 21010, one of the factors of 21010 other than 1 must be a perfect square. The factors of 21010 are 1, 2, 5, 10, 11, 22, 55, 110, 191, 382, 955, 1910, 2101, 4202, 10505, and 21010. Since none of these factors are perfect squares, the square root of 21010 cannot be simplified.

2) To be able to simplify the square root of 21010, all the prime factors of 21010 cannot be unique. When we did prime factorization of 21010, we found that 2 x 5 x 11 x 191 equals 21010. Since all the prime factors are unique, the square root of 21010 cannot be simplified.

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