Simplify Square Root of 84693

What is the square root of 84693 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.

√84693 = A√B

Unfortunately, the square root of 84693 cannot be simplified. Thus, here is the answer to the square root of 84693 in its simplest form:

√ 84693 = √ 84693

Here are two different methods we used to determine why the square root of 84693 cannot be simplified.

1) To be able to simplify the square root of 84693, one of the factors of 84693 other than 1 must be a perfect square. The factors of 84693 are 1, 3, 7, 21, 37, 109, 111, 259, 327, 763, 777, 2289, 4033, 12099, 28231, and 84693. Since none of these factors are perfect squares, the square root of 84693 cannot be simplified.

2) To be able to simplify the square root of 84693, all the prime factors of 84693 cannot be unique. When we did prime factorization of 84693, we found that 3 x 7 x 37 x 109 equals 84693. Since all the prime factors are unique, the square root of 84693 cannot be simplified.

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