Simplify Square Root of 34991

What is the square root of 34991 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.

√34991 = A√B

Unfortunately, the square root of 34991 cannot be simplified. Thus, here is the answer to the square root of 34991 in its simplest form:

√ 34991 = √ 34991

Here are two different methods we used to determine why the square root of 34991 cannot be simplified.

1) To be able to simplify the square root of 34991, one of the factors of 34991 other than 1 must be a perfect square. The factors of 34991 are 1, 11, 3181, and 34991. Since none of these factors are perfect squares, the square root of 34991 cannot be simplified.

2) To be able to simplify the square root of 34991, all the prime factors of 34991 cannot be unique. When we did prime factorization of 34991, we found that 11 x 3181 equals 34991. Since all the prime factors are unique, the square root of 34991 cannot be simplified.

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