Simplify Square Root of 93766

What is the square root of 93766 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.

√93766 = A√B

Unfortunately, the square root of 93766 cannot be simplified. Thus, here is the answer to the square root of 93766 in its simplest form:

√ 93766 = √ 93766

Here are two different methods we used to determine why the square root of 93766 cannot be simplified.

1) To be able to simplify the square root of 93766, one of the factors of 93766 other than 1 must be a perfect square. The factors of 93766 are 1, 2, 173, 271, 346, 542, 46883, and 93766. Since none of these factors are perfect squares, the square root of 93766 cannot be simplified.

2) To be able to simplify the square root of 93766, all the prime factors of 93766 cannot be unique. When we did prime factorization of 93766, we found that 2 x 173 x 271 equals 93766. Since all the prime factors are unique, the square root of 93766 cannot be simplified.

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