Simplify Square Root of 71681

What is the square root of 71681 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.

√71681 = A√B

Unfortunately, the square root of 71681 cannot be simplified. Thus, here is the answer to the square root of 71681 in its simplest form:

√ 71681 = √ 71681

Here are two different methods we used to determine why the square root of 71681 cannot be simplified.

1) To be able to simplify the square root of 71681, one of the factors of 71681 other than 1 must be a perfect square. The factors of 71681 are 1, 43, 1667, and 71681. Since none of these factors are perfect squares, the square root of 71681 cannot be simplified.

2) To be able to simplify the square root of 71681, all the prime factors of 71681 cannot be unique. When we did prime factorization of 71681, we found that 43 x 1667 equals 71681. Since all the prime factors are unique, the square root of 71681 cannot be simplified.

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