Simplify Square Root of 34993

What is the square root of 34993 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.

√34993 = A√B

Unfortunately, the square root of 34993 cannot be simplified. Thus, here is the answer to the square root of 34993 in its simplest form:

√ 34993 = √ 34993

Here are two different methods we used to determine why the square root of 34993 cannot be simplified.

1) To be able to simplify the square root of 34993, one of the factors of 34993 other than 1 must be a perfect square. The factors of 34993 are 1, 7, 4999, and 34993. Since none of these factors are perfect squares, the square root of 34993 cannot be simplified.

2) To be able to simplify the square root of 34993, all the prime factors of 34993 cannot be unique. When we did prime factorization of 34993, we found that 7 x 4999 equals 34993. Since all the prime factors are unique, the square root of 34993 cannot be simplified.

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