Simplify Square Root of 4105

What is the square root of 4105 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.

√4105 = A√B

Unfortunately, the square root of 4105 cannot be simplified. Thus, here is the answer to the square root of 4105 in its simplest form:

√ 4105 = √ 4105

Here are two different methods we used to determine why the square root of 4105 cannot be simplified.

1) To be able to simplify the square root of 4105, one of the factors of 4105 other than 1 must be a perfect square. The factors of 4105 are 1, 5, 821, and 4105. Since none of these factors are perfect squares, the square root of 4105 cannot be simplified.

2) To be able to simplify the square root of 4105, all the prime factors of 4105 cannot be unique. When we did prime factorization of 4105, we found that 5 x 821 equals 4105. Since all the prime factors are unique, the square root of 4105 cannot be simplified.

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