SOLUTION: square root of 72 plus square root of 18 minus the square root of -18

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Question 114967: square root of 72 plus square root of 18 minus the square root of -18
Answer by jgr45(31) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2872%29+sqrt%2818%29-sqrt%28-18%29
Find the prime factorization of each number. The factors of 72 are 3x3x2x2x2; the prime factors of 18 are 2x3x3. For each pair of factors, one of that number can move outside the radical. So sqrt%2872%29 becomes 3*2sqrt%282%29 or 6sqrt%282%29, and sqrt%2818%29 becomes 3sqrt%282%29.
Now, the square root of -18 (or any negative number) is something called a complex number. I'm not sure if you've studied that in your math/algebra classes, but the square root of -1 is defined to be i. So by definition, i%5E2 = -1. So that makes your square root of -18 to be 3isqrt%282%29.
Combine your coefficients and your answer is (9-3i)(sqrt%282%29).