Theory:

The decimal expansion of an irrational number is non-terminating and non-recurring. Conversely, the decimal expansion of a number is non-terminating and non-recurring is an irrational number.
Example:
Many square roots and cube roots are irrational numbers.
 
Let us find the square root of 5.
 
numbers_12.png
 
Thus, the decimal expansion of 5 have non-terminating and non-recurring decimals.
 
It goes like 5=2.2360...
 
3=1.7320508075...5=2.2360679774...33=1.4422495707...
Some of the famous irrational numbers:
 
Irrational Number
Its non-terminating and non-recurring decimal value
π(pi)\(3.141592653589793\)...
e(Eulersnumber)\(2.718281828459045\)...
ϕ(Goldenratio)\(1.618033988749894\)...