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 simplified form of (\frac{\sqrt{6}-\sqrt{2}}{\sqrt{6}+\sqrt{2}})?ExpertLevel 14A student claims that the product of two irrational numbers is always irrational. Which of the following examples disproves this claim?ExpertLevel 14What is the value of \(\sqrt{7}\left(\sqrt{175}-\sqrt{63}\right)\)?ExpertLevel 14Which of the following statements is necessarily true?ExpertLevel 14What is the rationalised form of 3/(√17 + √8)?MediumLevel 14Let \(a\) be a non-zero rational number and \(b\) be an irrational number. Which of the following statements is always true?ExpertLevel 14Which number definitely lies between (\sqrt{18}) and (\sqrt{20})?ExpertLevel 14Let \(p\) be a rational number and \(x\) be an irrational number. Which of the following statements is always true?ExpertLevel 14If \(r\) is a rational number and \(x\) is an irrational number, which of the following statements is always true?ExpertLevel 14What is the simplified form of (\sqrt{432}-\sqrt{192}+\sqrt{48})?ExpertLevel 14What is the value of (\frac{1}{\sqrt{7}+\sqrt{5}}+\frac{1}{\sqrt{7}-\sqrt{5}})?ExpertLevel 14If r is an irrational number and q is a rational number, which of the following expressions will always be irrational?ExpertLevel 14What is the value of (\frac{\sqrt{200}+\sqrt{72}}{\sqrt{2}})?ExpertLevel 14If (r=\sqrt{13}+\sqrt{7}) and (s=\sqrt{13}-\sqrt{7}), what is the value of (r^2-s^2)?ExpertLevel 14Which is the rationalised form of (\frac{8}{\sqrt{18}-\sqrt{10}})?ExpertLevel 14If (P=\sqrt{363}+\sqrt{108}-\sqrt{192}), what is (P) equal to?ExpertLevel 14What is the value of ((\sqrt{44}+\sqrt{99})^2)?ExpertLevel 14Which of the following expressions represents an irrational number?ExpertLevel 14Riya claims that \(0.101001000100001\ldots\) is rational because only the digits 0 and 1 occur in it. Which is the correct refutation of her claim?ExpertLevel 14What is the rationalised form of (\frac{5}{\sqrt{29}+2})?ExpertLevel 14