Question

What is the exact value of the expression 7sqrt(8) + 2 sqrt(12) - 3 sqrt(2)? Show your work

Answer 1

\[7\sqrt{8} + 2\sqrt{12} - 3\sqrt{2}\] Okay well to begin with, we cannot do anything with them yet because their square roots do not match. So I have to simplify them down so I can add and subtract them. The factors of 8 are 2*2*2 -- because we have 1 pair of 2's, they can come out. The factors of 12 are 3*2*2 -- again I have a pair of 2's so they can come out. That is all that I can simplify so now I have this equation:
\[14\sqrt{2} + 4\sqrt{3} - 3\sqrt{2}\] Combine the like square roots to make your final answer
\[11\sqrt{2}+4\sqrt{3}\]