Simplify Square Root of 74989

What is the square root of 74989 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.

√74989 = A√B

Unfortunately, the square root of 74989 cannot be simplified. Thus, here is the answer to the square root of 74989 in its simplest form:

√ 74989 = √ 74989

Here are two different methods we used to determine why the square root of 74989 cannot be simplified.

1) To be able to simplify the square root of 74989, one of the factors of 74989 other than 1 must be a perfect square. The factors of 74989 are 1, 31, 41, 59, 1271, 1829, 2419, and 74989. Since none of these factors are perfect squares, the square root of 74989 cannot be simplified.

2) To be able to simplify the square root of 74989, all the prime factors of 74989 cannot be unique. When we did prime factorization of 74989, we found that 31 x 41 x 59 equals 74989. Since all the prime factors are unique, the square root of 74989 cannot be simplified.

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