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 (s=\sqrt{75}+\sqrt{192}), what is the value of (\frac{s}{\sqrt{3}})?HardLevel 15Which is the simplified form of (\frac{\sqrt{7}-\sqrt{3}}{\sqrt{7}+\sqrt{3}})?HardLevel 15A student has written the following conclusions about irrational numbers. Which conclusion is always correct?HardLevel 15Which of the following options contains only irrational numbers?HardLevel 15If a rectangle has length (5+\sqrt{11}) and breadth (5-\sqrt{11}), what will be its area?HardLevel 15What is the simplified form of (\sqrt{500}-\sqrt{320}+\sqrt{180})?HardLevel 15What is the value of (\frac{1}{\sqrt{8}+\sqrt{6}}+\frac{1}{\sqrt{8}-\sqrt{6}})?HardLevel 15A student claims that the sum of two irrational numbers is always irrational. Which of the following expressions is a counterexample to the claim?HardLevel 15A student claims that the sum of any two irrational numbers is always irrational. Which of the following examples proves the claim wrong?HardLevel 15Let \(r\) be a rational number and \(x\) be an irrational number. Which of the following conclusions is always true?HardLevel 15Which number definitely lies between (\sqrt{14}) and (\sqrt{18})?HardLevel 15Let \(x\) be a non-zero irrational number, and let \(a\) and \(b\) be rational numbers, where \(b\ne0\). Which of the following expressions is always irrational?HardLevel 15What is the value of (\frac{\sqrt{200}-\sqrt{72}}{\sqrt{2}})?HardLevel 15What is the square of \(\sqrt{11+\sqrt{30}}\) equal to?HardLevel 15A student says, “The product of two irrational numbers is always irrational.” Which of the following examples proves this statement wrong?HardLevel 15What is the value of (√45 + √20)(√45 − √20)?MediumLevel 15Riya says that the quotient of two irrational numbers is always irrational. Which of the following examples proves her statement wrong?HardLevel 15Which is the simplified form of (\frac{\sqrt{11}+\sqrt{2}}{\sqrt{11}-\sqrt{2}})?HardLevel 15Let \(a\) be an irrational number and \(r\) be a non-zero rational number. Which of the following statements is always true?HardLevel 15What is the simplified form of (\sqrt{605}-\sqrt{245}+\sqrt{125})?HardLevel 15