Simplify Square Root of 41781

What is the square root of 41781 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.

√41781 = A√B

Unfortunately, the square root of 41781 cannot be simplified. Thus, here is the answer to the square root of 41781 in its simplest form:

√ 41781 = √ 41781

Here are two different methods we used to determine why the square root of 41781 cannot be simplified.

1) To be able to simplify the square root of 41781, one of the factors of 41781 other than 1 must be a perfect square. The factors of 41781 are 1, 3, 19, 57, 733, 2199, 13927, and 41781. Since none of these factors are perfect squares, the square root of 41781 cannot be simplified.

2) To be able to simplify the square root of 41781, all the prime factors of 41781 cannot be unique. When we did prime factorization of 41781, we found that 3 x 19 x 733 equals 41781. Since all the prime factors are unique, the square root of 41781 cannot be simplified.

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