Irrational numbers have been one of those chapters in mathematics which we have studied in different standards of our school. Can you recall it? Real numbers that cannot be expressed in the form of a simple fraction are known as irrational numbers. These are the numbers which cannot be represented in the form of ratio, p/q where p and q are integers and q is not equal to zero. Irrational numbers were introduced to make things easier. In absence of it, we will not have the continuum of real numbers which makes geometry, physics or engineering, either tough or impossible to do.
Irrational numbers are the subset of real numbers; thus, it will always obey all the properties of the real number system. You need to practice the below mentioned properties to understand it better. You can use different learning resources like Math worksheets on irrational numbers to practice these. The following properties ofirrational numbers are stated below:
- The addition of an irrational number and a rational number will always result in the formation of an irrational number. Let us take an example; assume x is a rational number and y is an irrational number, the result will be z which will be an irrational number.
- The multiplication of any irrational number with a non – zero rational number will result in the formation of an irrational number. Let us assume that xy=z is rational and x = z/y is rational, then this is contradicting the assumption that x is irrational. Thus, xy must be irrational.
- There is a high probability that the Least Common Multiple (LCM) of irrational numbers may or may not exist.
- If we multiply two irrational numbers, the result will be rational. For example, √3 3 is equal to 3 which shows that the result is rational. This property of irrational numbers is important, and you can practice more examples like these using Math worksheets.
- Under the multiplication process, the set of irrational numbers is not closed unlike that of rational numbers.
- The real numbers which cannot be expressed in the form of p/q where p and q are integers and q is not equal to zero is an irrational number.
- These are real numbers only.
- They are non-recurring and non-terminating decimals.
The irrational numbers are defined negatively. The set of real numbers that are not rational numbers are called irrational numbers, where real numbers are represented by the letter (R), rational numbers are represented by the capital letter (Q) and the irrational numbersare represented by the capital letter (P). These symbols are usually associated with irrational numbers, rational numbers and real numbers because of the alphabetic sequence P, Q, R. But mostly it is resented as the set difference of real minus rational in a way, R-Q and R /Q. Imaginary numbers are represented by the letter (I) and natural numbers by the letter (N).
In your school books or maths worksheets, you might have found various types of irrational numbers like √2, √3 and so on. However, there are certain irrational numbers which are quite famous but not known to everyone. Let us now discuss and learn about these numbers:
- Pi is an irrational number having the value of 22/7 or 3.14159265……
- Euler’s number, e is also an irrational number having the value of 2.178282828….
- Golden Ratio is also one the famous irrational numbers which comes under this list having the value of 1.618033… Golden Ratio is obtained with the help of Fibonacci sequence and is of extreme importance in our everyday life. Musicians and composers around the world use it to produce music. It is also used by investors and traders in technical analysis.
The best way to understand and learn about irrational numbers is using math worksheets. You can approach problems of irrational numbers step by step, recognize your mistakes and develop these concepts using worksheets. Math worksheets help students to grasp conceptual clarity and removes the fear that most of the students have for this subject. If you want to learn more about these interesting topics in a fun way, using math worksheets, do visit Cuemath.