Simplify Square Root of 49067

What is the square root of 49067 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.

√49067 = A√B

Unfortunately, the square root of 49067 cannot be simplified. Thus, here is the answer to the square root of 49067 in its simplest form:

√ 49067 = √ 49067

Here are two different methods we used to determine why the square root of 49067 cannot be simplified.

1) To be able to simplify the square root of 49067, one of the factors of 49067 other than 1 must be a perfect square. The factors of 49067 are 1, 139, 353, and 49067. Since none of these factors are perfect squares, the square root of 49067 cannot be simplified.

2) To be able to simplify the square root of 49067, all the prime factors of 49067 cannot be unique. When we did prime factorization of 49067, we found that 139 x 353 equals 49067. Since all the prime factors are unique, the square root of 49067 cannot be simplified.

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