Simplify Square Root of 85306

What is the square root of 85306 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.

√85306 = A√B

Unfortunately, the square root of 85306 cannot be simplified. Thus, here is the answer to the square root of 85306 in its simplest form:

√ 85306 = √ 85306

Here are two different methods we used to determine why the square root of 85306 cannot be simplified.

1) To be able to simplify the square root of 85306, one of the factors of 85306 other than 1 must be a perfect square. The factors of 85306 are 1, 2, 13, 17, 26, 34, 193, 221, 386, 442, 2509, 3281, 5018, 6562, 42653, and 85306. Since none of these factors are perfect squares, the square root of 85306 cannot be simplified.

2) To be able to simplify the square root of 85306, all the prime factors of 85306 cannot be unique. When we did prime factorization of 85306, we found that 2 x 13 x 17 x 193 equals 85306. Since all the prime factors are unique, the square root of 85306 cannot be simplified.

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