Simplify Square Root of 4709

What is the square root of 4709 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.

√4709 = A√B

Unfortunately, the square root of 4709 cannot be simplified. Thus, here is the answer to the square root of 4709 in its simplest form:

√ 4709 = √ 4709

Here are two different methods we used to determine why the square root of 4709 cannot be simplified.

1) To be able to simplify the square root of 4709, one of the factors of 4709 other than 1 must be a perfect square. The factors of 4709 are 1, 17, 277, and 4709. Since none of these factors are perfect squares, the square root of 4709 cannot be simplified.

2) To be able to simplify the square root of 4709, all the prime factors of 4709 cannot be unique. When we did prime factorization of 4709, we found that 17 x 277 equals 4709. Since all the prime factors are unique, the square root of 4709 cannot be simplified.

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