Simplify Square Root of 65641

What is the square root of 65641 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.

√65641 = A√B

Unfortunately, the square root of 65641 cannot be simplified. Thus, here is the answer to the square root of 65641 in its simplest form:

√ 65641 = √ 65641

Here are two different methods we used to determine why the square root of 65641 cannot be simplified.

1) To be able to simplify the square root of 65641, one of the factors of 65641 other than 1 must be a perfect square. The factors of 65641 are 1, 41, 1601, and 65641. Since none of these factors are perfect squares, the square root of 65641 cannot be simplified.

2) To be able to simplify the square root of 65641, all the prime factors of 65641 cannot be unique. When we did prime factorization of 65641, we found that 41 x 1601 equals 65641. Since all the prime factors are unique, the square root of 65641 cannot be simplified.

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