QUESTION

# State, with reason, which of the following are surds and which are not:(i)$\sqrt[3]{{25}}$(ii)$\sqrt[3]{{40}}$

(i) $\sqrt[3]{{25}}$ it is the cube root of 25.
And $\sqrt[3]{{25}}$=$\sqrt[3]{{5 \times 5}}$
Therefore we cannot express $\sqrt[3]{{25}}$ free of root so it’s surds.
(ii)$\sqrt[3]{{40}}$ it is the cube root of 40.
And $\sqrt[3]{{40}}$=$\sqrt[3]{{2 \times 2 \times 2 \times 5}}$
Therefore we cannot express $\sqrt[3]{{40}}$ free of root so it’s also surds.
Note – In this problem you need to know about surds. When we can't simplify a number to remove a square root (or cube root etc.) then it is a surd. Example: $\sqrt 2$ (square root of 2) can't be simplified further so it is a surd. Example: $\sqrt 4$ (square root of 4) can be simplified (to 2), so it is not a surd. Knowing this can solve your problem.