Simplify Square Root of 17630

What is the square root of 17630 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.

√17630 = A√B

Unfortunately, the square root of 17630 cannot be simplified. Thus, here is the answer to the square root of 17630 in its simplest form:

√ 17630 = √ 17630

Here are two different methods we used to determine why the square root of 17630 cannot be simplified.

1) To be able to simplify the square root of 17630, one of the factors of 17630 other than 1 must be a perfect square. The factors of 17630 are 1, 2, 5, 10, 41, 43, 82, 86, 205, 215, 410, 430, 1763, 3526, 8815, and 17630. Since none of these factors are perfect squares, the square root of 17630 cannot be simplified.

2) To be able to simplify the square root of 17630, all the prime factors of 17630 cannot be unique. When we did prime factorization of 17630, we found that 2 x 5 x 41 x 43 equals 17630. Since all the prime factors are unique, the square root of 17630 cannot be simplified.

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