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 option is the simplified form of √18?EasyLevel 16Which statement is correct about (2+\sqrt{5})?EasyLevel 16What is ( \sqrt{2}+\sqrt{2} ) equal to?EasyLevel 16Ravi says that \(\sqrt{49}\) is irrational because it has a square-root sign. Which statement correctly explains his error?EasyLevel 16Which option is the simplified form of √12?EasyLevel 16Which option is the simplified form of ( \sqrt{48} )?EasyLevel 16What type of number is ( \sqrt{3}\times\sqrt{12} )?EasyLevel 16Which is the simplified form of ( \sqrt{72} )?EasyLevel 16What type of number is ( -\sqrt{11} )?EasyLevel 16A student says that \(0.272727\ldots\) is irrational because its decimal expansion does not end. Which correction is correct?EasyLevel 16Which decimal is the form of an irrational number?EasyLevel 16What type of number is ( \frac{1}{\sqrt{2}} )?EasyLevel 16What type of number is (4-\sqrt{6})?EasyLevel 16Which option is the simplified form of ( \sqrt{108} )?EasyLevel 16Which number is irrational between (3) and (4)?EasyLevel 16What is the simplified form of ( \frac{\sqrt{18}}{3} )?EasyLevel 16Which number is called an irrational number?EasyLevel 17Which property does the decimal expansion of an irrational number have?EasyLevel 17Riya says that the sum of two irrational numbers is always irrational. Which of the following examples proves her statement wrong?EasyLevel 17Which statement is correct about √7?EasyLevel 17