Simplify Square Root of 77781

What is the square root of 77781 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.

√77781 = A√B

Unfortunately, the square root of 77781 cannot be simplified. Thus, here is the answer to the square root of 77781 in its simplest form:

√ 77781 = √ 77781

Here are two different methods we used to determine why the square root of 77781 cannot be simplified.

1) To be able to simplify the square root of 77781, one of the factors of 77781 other than 1 must be a perfect square. The factors of 77781 are 1, 3, 11, 33, 2357, 7071, 25927, and 77781. Since none of these factors are perfect squares, the square root of 77781 cannot be simplified.

2) To be able to simplify the square root of 77781, all the prime factors of 77781 cannot be unique. When we did prime factorization of 77781, we found that 3 x 11 x 2357 equals 77781. Since all the prime factors are unique, the square root of 77781 cannot be simplified.

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