Simplify Square Root of 57669

What is the square root of 57669 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.

√57669 = A√B

Unfortunately, the square root of 57669 cannot be simplified. Thus, here is the answer to the square root of 57669 in its simplest form:

√ 57669 = √ 57669

Here are two different methods we used to determine why the square root of 57669 cannot be simplified.

1) To be able to simplify the square root of 57669, one of the factors of 57669 other than 1 must be a perfect square. The factors of 57669 are 1, 3, 47, 141, 409, 1227, 19223, and 57669. Since none of these factors are perfect squares, the square root of 57669 cannot be simplified.

2) To be able to simplify the square root of 57669, all the prime factors of 57669 cannot be unique. When we did prime factorization of 57669, we found that 3 x 47 x 409 equals 57669. Since all the prime factors are unique, the square root of 57669 cannot be simplified.

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