   Question Answers

# State, with reason, which of the following are surds and which are not:(i)$\sqrt{{25}}$(ii)$\sqrt{{40}}$  Verified
112.5K+ Views
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) $\sqrt{{25}}$ it is the cube root of 25.
If we factorize 25 then we get 25 = 5x5
And $\sqrt{{25}}$=$\sqrt{{5 \times 5}}$
Therefore we cannot express $\sqrt{{25}}$ free of root so it’s surds.
(ii)$\sqrt{{40}}$ it is the cube root of 40.
If we factorize 25 then we get 40 = 2x2x2x5
And $\sqrt{{40}}$=$\sqrt{{2 \times 2 \times 2 \times 5}}$
Therefore we cannot express $\sqrt{{40}}$ 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.