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(i)$\sqrt[3]{{25}}$

(ii)$\sqrt[3]{{40}}$

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Hint – In order to solve this problem we need to understand that surd is a number that can't be simplified to remove a square root (or cube root etc.). Simplifying the given number you will know which is surd and which is not.

__Complete Step-by-Step solution:__

(i) $\sqrt[3]{{25}}$ it is the cube root of 25.

If we factorize 25 then we get 25 = 5x5

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.

If we factorize 25 then we get 40 = 2x2x2x5

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.

(i) $\sqrt[3]{{25}}$ it is the cube root of 25.

If we factorize 25 then we get 25 = 5x5

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.

If we factorize 25 then we get 40 = 2x2x2x5

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.