Simplify Square Root of 2165

What is the square root of 2165 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.

√2165 = A√B

Unfortunately, the square root of 2165 cannot be simplified. Thus, here is the answer to the square root of 2165 in its simplest form:

√ 2165 = √ 2165

Here are two different methods we used to determine why the square root of 2165 cannot be simplified.

1) To be able to simplify the square root of 2165, one of the factors of 2165 other than 1 must be a perfect square. The factors of 2165 are 1, 5, 433, and 2165. Since none of these factors are perfect squares, the square root of 2165 cannot be simplified.

2) To be able to simplify the square root of 2165, all the prime factors of 2165 cannot be unique. When we did prime factorization of 2165, we found that 5 x 433 equals 2165. Since all the prime factors are unique, the square root of 2165 cannot be simplified.

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