Simplify Square Root of 4609

What is the square root of 4609 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.

√4609 = A√B

Unfortunately, the square root of 4609 cannot be simplified. Thus, here is the answer to the square root of 4609 in its simplest form:

√ 4609 = √ 4609

Here are two different methods we used to determine why the square root of 4609 cannot be simplified.

1) To be able to simplify the square root of 4609, one of the factors of 4609 other than 1 must be a perfect square. The factors of 4609 are 1, 11, 419, and 4609. Since none of these factors are perfect squares, the square root of 4609 cannot be simplified.

2) To be able to simplify the square root of 4609, all the prime factors of 4609 cannot be unique. When we did prime factorization of 4609, we found that 11 x 419 equals 4609. Since all the prime factors are unique, the square root of 4609 cannot be simplified.

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