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 is the rationalised form of (\frac{5}{\sqrt{6}-1})?HardLevel 13What is the value of ((\sqrt{12}+\sqrt{27})^2)?HardLevel 13Which decimal can represent an irrational number?HardLevel 13A student says that \\(\frac{\sqrt{18}}{\sqrt{2}}\\) is irrational because it is the quotient of two irrational numbers. Which evaluation is correct?HardLevel 13What is the value of \(\sqrt{2}\left(\sqrt{50}-\sqrt{18}\right)\)?HardLevel 13What is the rationalised form of (\frac{2}{\sqrt{7}+\sqrt{5}})?HardLevel 13If x = 2√3 − √12, what is the value of x?EasyLevel 13What is the value of (\sqrt{3+\sqrt{2}}\times\sqrt{3+\sqrt{2}})?HardLevel 13Which is the simplified form of (\sqrt{98}+\sqrt{72}-\sqrt{8})?HardLevel 13Let \(x\) be an irrational number and \(r\) be a rational number. Which of the following expressions must be irrational?HardLevel 13If (s=\sqrt{27}+\sqrt{12}), what is the value of (\frac{s}{\sqrt{3}})?HardLevel 13Which is the simplified form of (\frac{\sqrt{3}-1}{\sqrt{3}+1})?HardLevel 13A student claims that the product of two non-zero irrational numbers is always irrational. Which of the following pairs provides a counterexample to the claim?HardLevel 13In which option is the result not rational?HardLevel 13Riya claims, “The square of every irrational number is also irrational.” Which of the following examples disproves her claim?HardLevel 13If a rectangle has length (3+\sqrt{2}) and breadth (3-\sqrt{2}), what will be its area?HardLevel 13What is the simplified form of (\sqrt{200}-\sqrt{128}+\sqrt{18})?HardLevel 13What is the value of 1/(√3 + √2) + 1/(√3 − √2)?HardLevel 13Riya says that \(\sqrt{45}+\sqrt{5}=\sqrt{50}\). Which is the correct evaluation of her statement?HardLevel 13If \(x\) is an irrational number, which of the following expressions will always be irrational?HardLevel 13