Simplify Square Root of 66769

What is the square root of 66769 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.

√66769 = A√B

Unfortunately, the square root of 66769 cannot be simplified. Thus, here is the answer to the square root of 66769 in its simplest form:

√ 66769 = √ 66769

Here are two different methods we used to determine why the square root of 66769 cannot be simplified.

1) To be able to simplify the square root of 66769, one of the factors of 66769 other than 1 must be a perfect square. The factors of 66769 are 1, 23, 2903, and 66769. Since none of these factors are perfect squares, the square root of 66769 cannot be simplified.

2) To be able to simplify the square root of 66769, all the prime factors of 66769 cannot be unique. When we did prime factorization of 66769, we found that 23 x 2903 equals 66769. Since all the prime factors are unique, the square root of 66769 cannot be simplified.

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