Question 114967
{{{sqrt(72)}}}+{{{sqrt(18)}}}-{{{sqrt(-18)}}}

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(72)}}} becomes 3*2{{{sqrt(2)}}} or 6{{{sqrt(2)}}}, and {{{sqrt(18)}}} becomes 3{{{sqrt(2)}}}.

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^2}}} = -1.  So that makes your square root of -18 to be 3i{{{sqrt(2)}}}.

Combine your coefficients and your answer is (9-3i)({{{sqrt(2)}}}).