Some Properties of Irrational Numbers
- Irrational numbers consist of non-terminating and non-recurring decimals.
- These are real numbers only.
- When an irrational and a rational number are added, the result or their sum is an irrational number only. For an irrational number x, and a rational number y, their result, x+y = an irrational number.
- When any irrational numbers multiplied by any non-zero rational number, their product is an irrational number. For an irrational number x and a rational number y, their product xy = irrational.
- For any two irrational numbers, their least common multiple (LCM) may or may not exist.
- Addition, subtraction, multiplication, and division of two irrational numbers may or may not be a rational numbers.
Some Irrational Numbers and their values are shown in the table below
| Irrational number | value |
| π | 3.14159265…. |
| e | 2.7182818….. |
| √2 | 1.414213562… |
| √3 | 1.73205080… |
| √5 | 2.23606797…. |
| √7 | 2.64575131…. |
| √11 | 3.31662479… |
| √13 | 3.605551275… |
| -√3/2 | -0.866025…. |
| ∛47 | 3.60882608 |