Simplify Square Root of 8189

What is the square root of 8189 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.

√8189 = A√B

Unfortunately, the square root of 8189 cannot be simplified. Thus, here is the answer to the square root of 8189 in its simplest form:

√ 8189 = √ 8189

Here are two different methods we used to determine why the square root of 8189 cannot be simplified.

1) To be able to simplify the square root of 8189, one of the factors of 8189 other than 1 must be a perfect square. The factors of 8189 are 1, 19, 431, and 8189. Since none of these factors are perfect squares, the square root of 8189 cannot be simplified.

2) To be able to simplify the square root of 8189, all the prime factors of 8189 cannot be unique. When we did prime factorization of 8189, we found that 19 x 431 equals 8189. Since all the prime factors are unique, the square root of 8189 cannot be simplified.

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