Simplify Square Root of 862

What is the square root of 862 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.

√862 = A√B

Unfortunately, the square root of 862 cannot be simplified. Thus, here is the answer to the square root of 862 in its simplest form:

√ 862 = √ 862

Here are two different methods we used to determine why the square root of 862 cannot be simplified.

1) To be able to simplify the square root of 862, one of the factors of 862 other than 1 must be a perfect square. The factors of 862 are 1, 2, 431, and 862. Since none of these factors are perfect squares, the square root of 862 cannot be simplified.

2) To be able to simplify the square root of 862, all the prime factors of 862 cannot be unique. When we did prime factorization of 862, we found that 2 x 431 equals 862. Since all the prime factors are unique, the square root of 862 cannot be simplified.

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