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Irrational numbers are real numbers which are not perfect fractions. This means that irrational numbers cannot be represented as a complete fraction or ratios. The unique property of irrational numbers is that their decimal expansion is non-terminating and non-repeating. General rules of arithmetic operations cannot be applied directly to irrational numbers. The irrational numbers need to be solved first (decimal values) and then they can be either added, subtracted, multiplied or divided.
Some of the most important and popular irrational numbers are π (Pi), √2 (Square Root of 2) and e (Euler’s Number). Irrational numbers belong to the set of real numbers and are represented as a set {R-Q} where R is a set of real numbers and Q is a set of integers. Let us know more about irrational numbers!
A Greek mathematician, Hippasus of Metapontum was baffled when he realised that in a right angled isosceles triangle, whose base side and perpendicular are 1 unit in length, has a hypotenuse length of √2 which is an irrational number. Unfortunately, this discovery led to the demise of the mathematician as he was thrown in the sea! He was a member of a society (‘Pythagoreans’) which believed that whole numbers and their ratios was the ultimate truth!
Few hundred years later, a German mathematician, Georg Cantor provided a definite proof for the existence of irrational numbers. He proved that both rational and irrational numbers are countable, while real numbers are uncountable.
This story proves that mathematics is scary, right?
Irrational numbers are not scary. As a matter of fact, discovery of irrational numbers led to the application of π as one of the most important constants in scientific world. Similarly, the irrational numbers help in proving various theories and solving complex equations which involve multiple variables.
The concept of irrational numbers and their applications are very important for students of science and engineering. The sections dealing with irrational numbers must be dealt with very carefully as questions based on irrational numbers form the base of theories of Classical Mechanics and Quantum Physics!
Let us now understand what are the defining properties of irrational numbers which make them so unique.
For students studying in various secondary and higher secondary education boards of India, the concept of irrational numbers is introduced from early classes. The idea is to help students understand the properties and identification of irrational numbers from an early age, which helps in development of a solid foundation for advanced mathematics.
In essence, the questions based on irrational number are easy to moderately difficult. This depends a lot on consistent practise of basic and tricky questions. At Embibe, you can learn the concepts of irrational numbers, practise exercises regularly and finally test your ability to solve questions quickly. The students can find the mock tests on the Embibe Learning and Outcomes App to improve their classroom performance!
Stay tuned to Embibe to catch interesting insights on more such topics!
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