Simplify Square Root of 3409

What is the square root of 3409 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.

√3409 = A√B

Unfortunately, the square root of 3409 cannot be simplified. Thus, here is the answer to the square root of 3409 in its simplest form:

√ 3409 = √ 3409

Here are two different methods we used to determine why the square root of 3409 cannot be simplified.

1) To be able to simplify the square root of 3409, one of the factors of 3409 other than 1 must be a perfect square. The factors of 3409 are 1, 7, 487, and 3409. Since none of these factors are perfect squares, the square root of 3409 cannot be simplified.

2) To be able to simplify the square root of 3409, all the prime factors of 3409 cannot be unique. When we did prime factorization of 3409, we found that 7 x 487 equals 3409. Since all the prime factors are unique, the square root of 3409 cannot be simplified.

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