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 says, “The sum of two irrational numbers is always irrational.” Which of the following examples proves this statement wrong?MediumLevel 14Which statement correctly describes the decimal expansion of an irrational number?MediumLevel 14What is the simplified value of (\frac{\sqrt{150}+\sqrt{54}}{\sqrt{6}})?MediumLevel 14A 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 this statement?MediumLevel 14What is the simplified form of (\sqrt{10}(3\sqrt{10}-2\sqrt{40}))?MediumLevel 14Which option is the correct rationalised form of (\frac{6}{\sqrt{19}})?MediumLevel 14Which statement is correct about (\sqrt{12}+\sqrt{108}) and (8\sqrt{3})?MediumLevel 14What type of number is the decimal (5.12012001200012\ldots)?MediumLevel 14What is the rationalised form of (\frac{1}{5+\sqrt{6}})?MediumLevel 14Aman called the decimal 0.101001000100001... a rational number because it contains only the digits 0 and 1. What is the error in Aman’s conclusion?MediumLevel 15Which is the simplified form of (\sqrt{48}+\sqrt{27})?MediumLevel 15A student writes the number \(0.101001000100001\ldots\), in which the number of zeros before each successive 1 keeps increasing. Which statement about this number is correct?MediumLevel 15What is obtained by rationalising 1/(√6 + 1)?MediumLevel 15Riya says that \(\sqrt{n}\) is irrational for every natural number n. Which of the following examples proves her statement wrong?MediumLevel 15Reema claims that the sum of two irrational numbers is always irrational. Which of the following examples disproves her claim?MediumLevel 15Which is the simplified form of (\sqrt{98}-\sqrt{50})?MediumLevel 15What is the simplified form of (\sqrt{7}+\sqrt{28}+\sqrt{63})?MediumLevel 15What type of number is the decimal (0.404004000400004\ldots)?MediumLevel 15What is the value of \(\left(\frac{\sqrt{108}}{\sqrt{3}}\right)\)?MediumLevel 15Which is the simplified form of (\sqrt{162}+\sqrt{72})?MediumLevel 15