Simplify Square Root of 21535

What is the square root of 21535 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.

√21535 = A√B

Unfortunately, the square root of 21535 cannot be simplified. Thus, here is the answer to the square root of 21535 in its simplest form:

√ 21535 = √ 21535

Here are two different methods we used to determine why the square root of 21535 cannot be simplified.

1) To be able to simplify the square root of 21535, one of the factors of 21535 other than 1 must be a perfect square. The factors of 21535 are 1, 5, 59, 73, 295, 365, 4307, and 21535. Since none of these factors are perfect squares, the square root of 21535 cannot be simplified.

2) To be able to simplify the square root of 21535, all the prime factors of 21535 cannot be unique. When we did prime factorization of 21535, we found that 5 x 59 x 73 equals 21535. Since all the prime factors are unique, the square root of 21535 cannot be simplified.

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