On this page you will get Information about Irrational Numbers. So definitely read the post completely.
On the previous page, I have shared information about Composite Numbers, Prime Numbers and Co-Prime Numbers, so you can get all the information by reading those posts.
Let us read and understand the information on Irrational Number on this page.
What are Irrational Number
If the square of a number is a negative number, then such number are called Irrational Number.
In other words – numbers made up of Real Numbers and Unreal Number are Called Unreal numbers.
Example :- √-3, √-5, √-3/4, √7/-13, √11/-17.
Real numbers are written as :- √-3, √-5, √-3/4, √7/-13, √11/-17.
How to Identify Irrational Number
Irrational numbers are real number that are not rational, i.e., cannot be expressed as a fraction p/q.
Where, p and q are integers such that q ≠ 0, number which cannot be expressed in the form of irrational number are called irrational number.
Irrational number are always written as ( √ ).
Like :- √2, √5, √7, √33 √73……….
Properties of Irrational Number
1. When two numbers, one rational and one irrational, are added, we get irrational number.
As :-
- 3 + 4√5 = 3 + 4√5 (These are irrational number.)
- 5√3 + 7√3 = 10√3 (These are irrational number.)
2. If a rational number and an irrational number are multiplied, we will get an irrational number only.
As :-
- 5 × 2√3 = 10√3 (These are irrational number.)
- 3√2 × 4 = 12√2 (These are irrational number.)
3. The product of two irrational number can be either rational or irrational number.
As :-
- √5 × 2√5 = 10 (It is a rational number.)
- 3√7 × 4√7 = 84 (It is a rational number.)
4. The least of more than one irrational number may be rational or Irrational Number.
Famous Irrational Number
There are many numbers in mathematical numbers that can be written as Irrational Number.
For Example :- √2, √5, √17, √29 etc.
But there are many numbers which cannot be written in the form of irrational number, so the famous irrational number are shown below.
But there are many number which cannot be written in the form of irrational number, so the famous irrational number are shown below.
| π | 22/7 = 3.1428571428571 |
| e | 2.718281828 |
| φ | 1.61803398874989484820… |
| √2 | 1.4142135623 |
| √3 | 1.7320508075 |
| √5 | 2.2360679774 |
Irrational Number Questions and Answers
Question 1. What are irrational number?
Answer :- Number which cannot be written in the form of p/q are called irrational number. As; π, φ, √5, √7, √13 etc.
Question 2. Is π (pi) an irrational number?
Answer :- π is a mathematical constant whose numerical value is equal to the ratio of the circumference of a circle to its diameter, yet the numerical value of π is not known, so it is considered an irrational number.
Question 3. Are √2 and √3 irrational number?
Answer :- Yes, both of these are irrational number because they cannot be written in the form of ratio i.e. in the form of p/q.
Question 4. Is √1 an irrational number?
Answer :- √1 is not an irrational number because √1 is a perfect square. which can be written as 1/1.
Question 5. Is √16 a rational number?
Answer :- Yes, √16 is a rational number because √16 is a perfect square. The square root of √16 is 4, which is a rational number that can be written in the form (4/1).
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FAQ
Ans. An irrational number is a real number that cannot be expressed as a ratio of integers
Ans. It is irrational because it cannot be written as a ratio (or fraction),
Ans. (1). lacking usual or normal mental clarity or coherence. (2). not endowed with reason or understanding.
Ans. A rational number, in Mathematics, can be defined as any number which can be represented in the form of p/q where q ≠ 0.
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