Simplify Square Root of 3646

What is the square root of 3646 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.

√3646 = A√B

Unfortunately, the square root of 3646 cannot be simplified. Thus, here is the answer to the square root of 3646 in its simplest form:

√ 3646 = √ 3646

Here are two different methods we used to determine why the square root of 3646 cannot be simplified.

1) To be able to simplify the square root of 3646, one of the factors of 3646 other than 1 must be a perfect square. The factors of 3646 are 1, 2, 1823, and 3646. Since none of these factors are perfect squares, the square root of 3646 cannot be simplified.

2) To be able to simplify the square root of 3646, all the prime factors of 3646 cannot be unique. When we did prime factorization of 3646, we found that 2 x 1823 equals 3646. Since all the prime factors are unique, the square root of 3646 cannot be simplified.

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