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
A student calls the number \(0.101001000100001\ldots\) rational because it contains only the digits 0 and 1. What is the correct conclusion?MediumLevel 13What is the simplified form of \((\sqrt{2}\times(3\sqrt{2}+1))\)?MediumLevel 13Which is the rationalised form of (\frac{3}{\sqrt{2}+1})?MediumLevel 13What is the sum of \((7+\sqrt{13})\) and \((7-\sqrt{13})\)?MediumLevel 13Ravi claims that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. What is the correct evaluation of his claim?MediumLevel 13If (p=4+\sqrt{5}), what type of number is (p)?MediumLevel 13What type of number is (\sqrt{2}\times\sqrt{8})?MediumLevel 13If the area of a square is (18) square units, what will be the simplified form of its side?MediumLevel 13Riya claims that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which statement correctly explains Riya’s error?MediumLevel 13Which statement is correct about (\sqrt{3}+\sqrt{27}) and (\sqrt{48})?MediumLevel 13What is the simplified form of (2\sqrt{5}+3\sqrt{20})?MediumLevel 13Reema says that the number \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. What is the correct evaluation of Reema’s statement?MediumLevel 13Which is the simplified form of \((\sqrt{2}+\sqrt{32})\)?MediumLevel 13Riya says, “Any number with an infinite decimal expansion must be irrational.” Which example proves Riya’s statement wrong?MediumLevel 13Which option shows correct rationalisation of the denominator?MediumLevel 13If (r=\sqrt{15}-\sqrt{6}) and (s=\sqrt{15}+\sqrt{6}), what is the value of (rs)?MediumLevel 13What is the simplified value of (\frac{\sqrt{98}+\sqrt{50}}{\sqrt{2}})?MediumLevel 13A student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. What is the correct evaluation of the student's statement?MediumLevel 13What is the simplified form of (\sqrt{5}(2\sqrt{5}-3\sqrt{20}))?MediumLevel 13Which option is an equal form of an irrational number with a rationalised denominator?MediumLevel 13