Simplify Square Root of 85394

What is the square root of 85394 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.

√85394 = A√B

Unfortunately, the square root of 85394 cannot be simplified. Thus, here is the answer to the square root of 85394 in its simplest form:

√ 85394 = √ 85394

Here are two different methods we used to determine why the square root of 85394 cannot be simplified.

1) To be able to simplify the square root of 85394, one of the factors of 85394 other than 1 must be a perfect square. The factors of 85394 are 1, 2, 42697, and 85394. Since none of these factors are perfect squares, the square root of 85394 cannot be simplified.

2) To be able to simplify the square root of 85394, all the prime factors of 85394 cannot be unique. When we did prime factorization of 85394, we found that 2 x 42697 equals 85394. Since all the prime factors are unique, the square root of 85394 cannot be simplified.

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