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Irrational Number are real numbers that cannot be written as a simple fraction and have decimal expansions that neither terminate nor become periodic. For example pi ( (3.1415...) is an irrational number as it has an infinite number of digits after the decimal point. In the same way 3^1/2 = 1.732..... is irrational as its decimal expansion neither terminates  nor become periodic.

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Any number that cannot be expressed as a rational of 2 integers is called a irrational number. If I take Pi, the value of Pi is 3.14159.....So the value of Pi doesn't stop at 3.14 but it goes beyond. So this is a irrational number. And if you look at the square root value of 2. It goes beyond 1.41421356...... So square root of 2 is an irrational number. But if you look at square root of 9, it is 3. It is exactly 3. And so it is a rational number. Square root value of 3, 5, 7, 10 are also examples of irrational numbers.