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
Which sum is irrational?ExpertLevel 2Which number has a non-terminating non-recurring decimal?ExpertLevel 2Which number lies between two irrational numbers?ExpertLevel 2If (p) is rational and (q) is irrational then (p+q) is?ExpertLevel 2Which number is closest to (\sqrt{17})?ExpertLevel 2Which difference is irrational?ExpertLevel 2What is the value of (\sqrt{48}+\sqrt{75})?ExpertLevel 3Which number is closest to (\sqrt{50})?ExpertLevel 3If (p) is rational and (q) is irrational then (pq) can be?ExpertLevel 3If (a=\sqrt{98}) and (b=\sqrt{50}), what is (a-b)?ExpertLevel 3Which type of decimal expansion identifies an irrational number?EasyLevel 16Which number cannot be written in the form ( \frac{p}{q} )?EasyLevel 16Riya claims that the sum of any two irrational numbers is always irrational. Which of the following examples proves her claim wrong?EasyLevel 16What type of number is ( \sqrt{8} )?EasyLevel 16Which is an example of an irrational number?EasyLevel 16Sonam says that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. Which response is correct?EasyLevel 16Which number will have a non-terminating non-recurring decimal?EasyLevel 16What is the correct statement about ( \sqrt{50} )?EasyLevel 16In which option are both numbers irrational?EasyLevel 16Which is the correct characteristic of the decimal expansion of an irrational number?EasyLevel 16