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
If u = √125 − √45 and v = √5, what is the value of u − v?MediumLevel 14Which is the rationalised form of (\frac{4}{\sqrt{10}-\sqrt{6}})?HardLevel 14What is the value of ((\sqrt{20}+\sqrt{45})^2)?HardLevel 14A student claims that the quotient of any two irrational numbers is always irrational. Which of the following calculations conclusively proves the claim wrong?HardLevel 14What is the value of \(\sqrt{3}\left(\sqrt{75}-\sqrt{27}\right)\)?HardLevel 14What is the rationalised form of (\frac{3}{\sqrt{8}+\sqrt{5}})?HardLevel 14If an irrational number is added to a rational number, what will the resulting number always be?HardLevel 14What is the value of √(4 + √7) × √(4 + √7)?EasyLevel 14Which is the simplified form of (\sqrt{162}+\sqrt{98}-\sqrt{50})?HardLevel 14If t = √7 + 2, what is the value of t + 3/t?MediumLevel 14If (s=\sqrt{48}+\sqrt{75}), what is the value of (\frac{s}{\sqrt{3}})?HardLevel 14Which is the simplified form of (\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}})?HardLevel 14For a positive integer \(n\), which criterion correctly determines that \(\sqrt{n}\) is irrational?HardLevel 14Reema claims that the product of two irrational numbers is always irrational. Which of the following examples disproves her claim?HardLevel 14If a rectangle has length (4+\sqrt{5}) and breadth (4-\sqrt{5}), what will be its area?HardLevel 14What is the simplified form of (\sqrt{300}-\sqrt{192}+\sqrt{75})?HardLevel 14What is the value of (\frac{1}{\sqrt{5}+\sqrt{3}}+\frac{1}{\sqrt{5}-\sqrt{3}})?HardLevel 14Reena claims, “The sum of two irrational numbers is always irrational.” Which of the following pairs disproves her claim?HardLevel 14In which option are both numbers irrational, but their sum is rational?HardLevel 14Ravi claims that \(x=\frac{3+\sqrt{2}}{5}\) is rational because its denominator is 5. What is the error in Ravi’s claim?HardLevel 14