Simplify Square Root of 10165

What is the square root of 10165 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.

√10165 = A√B

Unfortunately, the square root of 10165 cannot be simplified. Thus, here is the answer to the square root of 10165 in its simplest form:

√ 10165 = √ 10165

Here are two different methods we used to determine why the square root of 10165 cannot be simplified.

1) To be able to simplify the square root of 10165, one of the factors of 10165 other than 1 must be a perfect square. The factors of 10165 are 1, 5, 19, 95, 107, 535, 2033, and 10165. Since none of these factors are perfect squares, the square root of 10165 cannot be simplified.

2) To be able to simplify the square root of 10165, all the prime factors of 10165 cannot be unique. When we did prime factorization of 10165, we found that 5 x 19 x 107 equals 10165. Since all the prime factors are unique, the square root of 10165 cannot be simplified.

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