Simplify Square Root of 49971

What is the square root of 49971 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.

√49971 = A√B

Unfortunately, the square root of 49971 cannot be simplified. Thus, here is the answer to the square root of 49971 in its simplest form:

√ 49971 = √ 49971

Here are two different methods we used to determine why the square root of 49971 cannot be simplified.

1) To be able to simplify the square root of 49971, one of the factors of 49971 other than 1 must be a perfect square. The factors of 49971 are 1, 3, 16657, and 49971. Since none of these factors are perfect squares, the square root of 49971 cannot be simplified.

2) To be able to simplify the square root of 49971, all the prime factors of 49971 cannot be unique. When we did prime factorization of 49971, we found that 3 x 16657 equals 49971. Since all the prime factors are unique, the square root of 49971 cannot be simplified.

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