Simplify Square Root of 7721

What is the square root of 7721 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.

√7721 = A√B

Unfortunately, the square root of 7721 cannot be simplified. Thus, here is the answer to the square root of 7721 in its simplest form:

√ 7721 = √ 7721

Here are two different methods we used to determine why the square root of 7721 cannot be simplified.

1) To be able to simplify the square root of 7721, one of the factors of 7721 other than 1 must be a perfect square. The factors of 7721 are 1, 7, 1103, and 7721. Since none of these factors are perfect squares, the square root of 7721 cannot be simplified.

2) To be able to simplify the square root of 7721, all the prime factors of 7721 cannot be unique. When we did prime factorization of 7721, we found that 7 x 1103 equals 7721. Since all the prime factors are unique, the square root of 7721 cannot be simplified.

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