Question

Which of the following is irrational? √27 1/3 √0.16 √(25/64)​

Answer 1

Step-by-step explanation:

If decimal expansion of number terminate or non terminate but repeat some pattern. It will be rational number. Let us see option;

Option (a) = 0.15

Its decimal expansion is terminate, so it is rational number.

Option (b) = 0.01516

Its decimal expansion is terminate, so it is rational number.

Option (c) = 0.15161516...

Its decimal expansion is non-terminate but it is repeating. Repeating pattern are 1516. So it is rational number.

Irrational number:-

If decimal expansion of number is non terminate also non repeating of some pattern. It will be irrational number. Let us see option;

Option (d) = 0.15161516...

Its decimal expansion is neither non-terminate nor repeating. So it is irrational number.

So option d is irrational number.