Simplify Square Root of 843

What is the square root of 843 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.

√843 = A√B

Unfortunately, the square root of 843 cannot be simplified. Thus, here is the answer to the square root of 843 in its simplest form:

√ 843 = √ 843

Here are two different methods we used to determine why the square root of 843 cannot be simplified.

1) To be able to simplify the square root of 843, one of the factors of 843 other than 1 must be a perfect square. The factors of 843 are 1, 3, 281, and 843. Since none of these factors are perfect squares, the square root of 843 cannot be simplified.

2) To be able to simplify the square root of 843, all the prime factors of 843 cannot be unique. When we did prime factorization of 843, we found that 3 x 281 equals 843. Since all the prime factors are unique, the square root of 843 cannot be simplified.

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