Simplify Square Root of 2158

What is the square root of 2158 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.

√2158 = A√B

Unfortunately, the square root of 2158 cannot be simplified. Thus, here is the answer to the square root of 2158 in its simplest form:

√ 2158 = √ 2158

Here are two different methods we used to determine why the square root of 2158 cannot be simplified.

1) To be able to simplify the square root of 2158, one of the factors of 2158 other than 1 must be a perfect square. The factors of 2158 are 1, 2, 13, 26, 83, 166, 1079, and 2158. Since none of these factors are perfect squares, the square root of 2158 cannot be simplified.

2) To be able to simplify the square root of 2158, all the prime factors of 2158 cannot be unique. When we did prime factorization of 2158, we found that 2 x 13 x 83 equals 2158. Since all the prime factors are unique, the square root of 2158 cannot be simplified.

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