Question

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`

Answer 1

(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.