Simplify Square Root of 74089

What is the square root of 74089 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.

√74089 = A√B

Unfortunately, the square root of 74089 cannot be simplified. Thus, here is the answer to the square root of 74089 in its simplest form:

√ 74089 = √ 74089

Here are two different methods we used to determine why the square root of 74089 cannot be simplified.

1) To be able to simplify the square root of 74089, one of the factors of 74089 other than 1 must be a perfect square. The factors of 74089 are 1, 43, 1723, and 74089. Since none of these factors are perfect squares, the square root of 74089 cannot be simplified.

2) To be able to simplify the square root of 74089, all the prime factors of 74089 cannot be unique. When we did prime factorization of 74089, we found that 43 x 1723 equals 74089. Since all the prime factors are unique, the square root of 74089 cannot be simplified.

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