Simplify Square Root of 40078

What is the square root of 40078 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.

√40078 = A√B

Unfortunately, the square root of 40078 cannot be simplified. Thus, here is the answer to the square root of 40078 in its simplest form:

√ 40078 = √ 40078

Here are two different methods we used to determine why the square root of 40078 cannot be simplified.

1) To be able to simplify the square root of 40078, one of the factors of 40078 other than 1 must be a perfect square. The factors of 40078 are 1, 2, 29, 58, 691, 1382, 20039, and 40078. Since none of these factors are perfect squares, the square root of 40078 cannot be simplified.

2) To be able to simplify the square root of 40078, all the prime factors of 40078 cannot be unique. When we did prime factorization of 40078, we found that 2 x 29 x 691 equals 40078. Since all the prime factors are unique, the square root of 40078 cannot be simplified.

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