Mathematics
Irrational numbers
अपरिमेय संख्याएँ
In this Class 9 Mathematics topic from the Number Systems chapter, students learn that irrational numbers cannot be written in the form p/q, where p and q are integers and q is not zero. They explore familiar examples such as √2 and π, understand their non-terminating, non-repeating decimal expansions, and distinguish them from rational numbers. The topic also develops skills for representing irrational numbers on the number line and understanding their place within the real number system.
Practice questions
A student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. Which option correctly explains the student's error?EasyLevel 18While locating \(\sqrt{5}\) on the number line, which conclusion about its position and type is correct?EasyLevel 18Which of these is an irrational number between 1 and 3?EasyLevel 18What type of number is (6-\sqrt{2})?EasyLevel 18What is the simplified form of \((\sqrt{7}+\sqrt{7})\)?EasyLevel 18Which is the simplified form of (\sqrt{12}+\sqrt{75})?EasyLevel 18What is the simplified form of (\sqrt{80}-\sqrt{45})?EasyLevel 18Riya says that the number 0.101001000100001… is rational because it contains only the digits 0 and 1. Which option correctly evaluates Riya’s statement?EasyLevel 18How can (\frac{1}{\sqrt{3}}) be written after removing the radical from the denominator?EasyLevel 18Which option is a rational number?EasyLevel 18What type of number is π + 2?EasyLevel 18If a number has decimal (4.10110111011110\ldots), what is it?EasyLevel 18What type of number is (\sqrt{\frac{7}{4}})?EasyLevel 18A student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. Which is the correct correction to the student's statement?EasyLevel 18What type of number is \((-3\sqrt{11})\)?EasyLevel 18Which of the following statements correctly describes the decimal expansion of an irrational number?EasyLevel 18Which is the reciprocal of √13?EasyLevel 18What is the value of ((\sqrt{2}+1)-\sqrt{2})?EasyLevel 18What is the value of ((\sqrt{6}+2)(\sqrt{6}-2))?EasyLevel 18A student says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which conclusion is correct?EasyLevel 18