Question 342910
Let sqrt = square root for short



sqrt[32] + 3(sqrt[8]) - 4(sqrt[18]) =



Break down every square root.  Your goal is to get the same radicand for every term.


sqrt[32] = 8(sqrt[2])



3(sqrt[8]) = 6(sqrt[2])



4(sqrt[18]) = 12(sqrt[2])



We now have 8(sqrt[2]) + 6(sqrt[2]) - 12(sqrt[2])



Notice how every radical has the same number 2.  This was the goal. 



We now simplify 8(sqrt[2]) + 6(sqrt[2]) - 12(sqrt[2]).



8(sqrt[2]) + 6(sqrt[2]) - 12(sqrt[2]) = 14(sqrt[2]) - 12(sqrt[2]).




14(sqrt[2]) - 12(sqrt[2]) = 2(sqrt[2]) as the final answer.



Did you follow?