Simplify Square Root of 74722

What is the square root of 74722 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.

√74722 = A√B

Unfortunately, the square root of 74722 cannot be simplified. Thus, here is the answer to the square root of 74722 in its simplest form:

√ 74722 = √ 74722

Here are two different methods we used to determine why the square root of 74722 cannot be simplified.

1) To be able to simplify the square root of 74722, one of the factors of 74722 other than 1 must be a perfect square. The factors of 74722 are 1, 2, 37361, and 74722. Since none of these factors are perfect squares, the square root of 74722 cannot be simplified.

2) To be able to simplify the square root of 74722, all the prime factors of 74722 cannot be unique. When we did prime factorization of 74722, we found that 2 x 37361 equals 74722. Since all the prime factors are unique, the square root of 74722 cannot be simplified.

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