InterviewSolution
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InterviewSolution
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Classify the following numbers as rational or irrational:(i) `2-sqrt(5)` (ii) `(3+sqrt(23))-sqrt(23)` (iii) `(2sqrt(7))/(7sqrt(7))` (iv) `1/(sqrt(2))` (v) `2pi` |
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Answer» (i) `2-sqrt(5) = 2-2.23606797... = -0.23606797...`Since, decimal representation of this number is non-terminating, it is an irrational number. (ii)`(3+sqrt(23))-sqrt23 = 3 = 3/1`Since, the above number can be represented as `p/q`, where both `p` and `q` are integers, this number is rational number. (iii)`(2sqrt7)/(7sqrt7) = 2/7`Since, the above number can be represented as `p/q`, where both `p` and `q` are integers, this number is rational number. (iv)`1/sqrt2 = 0.70710678...` Since, decimal representation of this number is non-terminating, it is an irrational number. (v)`2pi = 2(3.14159265...) = 6.28318530...` Since, decimal representation of this number is non-terminating, it is an irrational number. |
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