SOLUTION: what is 4 times the square root of 2 plus 3 times the square root of 8?

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Question 720688: what is 4 times the square root of 2 plus 3 times the square root of 8?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
4sqrt%282%29+%2B+3sqrt%288%29
Like radical terms have the same kinds of roots with the same radicands. ("Radicand" is the name for the expression inside a radical.) So these are not like terms and cannot be added (yet).

But the second square root's radicand has a perfect square factor so it will simplify:
4sqrt%282%29+%2B+3sqrt%284%2A2%29
4sqrt%282%29+%2B+3sqrt%284%29%2Asqrt%282%29
4sqrt%282%29+%2B+3%2A2%2Asqrt%282%29
4sqrt%282%29+%2B+6sqrt%282%29
After simplifying, we find that we now have like terms. (Both are square roots and both radicands are 2's.) So we can add them. And exactly like 4x + 6x = 10x:
4sqrt%282%29+%2B+6sqrt%282%29
adds up to
10sqrt%282%29