Simplify Square Root of 80538

What is the square root of 80538 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.

√80538 = A√B

Unfortunately, the square root of 80538 cannot be simplified. Thus, here is the answer to the square root of 80538 in its simplest form:

√ 80538 = √ 80538

Here are two different methods we used to determine why the square root of 80538 cannot be simplified.

1) To be able to simplify the square root of 80538, one of the factors of 80538 other than 1 must be a perfect square. The factors of 80538 are 1, 2, 3, 6, 31, 62, 93, 186, 433, 866, 1299, 2598, 13423, 26846, 40269, and 80538. Since none of these factors are perfect squares, the square root of 80538 cannot be simplified.

2) To be able to simplify the square root of 80538, all the prime factors of 80538 cannot be unique. When we did prime factorization of 80538, we found that 2 x 3 x 31 x 433 equals 80538. Since all the prime factors are unique, the square root of 80538 cannot be simplified.

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