Summary on Irrational Numbers
- Terminating and repeating decimals are classified as rational numbers because they can be expressed as fractions. On the other hand, irrational numbers are numbers that are neither repeating nor terminating. Examples include numbers like $0.121221222…$.
- $\pi$ is also an irrational number.
- The sum of an irrational number and a rational number is always irrational.
- The product of an irrational number and a rational number is always irrational. if the rational number is different from zero.
- When an irrational number is divided by non – zero rational number is always irrational.
- The difference between an irrational number and a rational number is always irrational.
- Irrational numbers cannot be expressed as a fraction of two integers.
- A number that can not be written out of nth root is an irrational number. example $\sqrt{46}$, $\sqrt[3]{9}, ….$ are an irrational numbers because it cannot be simplified further.
- The set of irrational numbers is not closed under addition, subtraction, multiplication and division.