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 number lies between (\sqrt{21}) and (\sqrt{30})?MediumLevel 15A student says that 0.101001000100001… is rational because it contains only the digits 0 and 1. What is the correct evaluation of this statement?MediumLevel 15Reema says that every non-terminating decimal is an irrational number. Which of the following examples shows the error in her statement?MediumLevel 15What is the rationalised form of (\frac{7}{\sqrt{3}})?MediumLevel 15What is the value of (√12 + √3)^2?MediumLevel 15Riya says that the number \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1, and the number of zeros between successive 1s keeps increasing by one. What is the correct evaluation of Riya's statement?MediumLevel 15What is the simplified form of (\sqrt{147}+\sqrt{75}-\sqrt{27})?MediumLevel 15Rahul says that every number with an infinite decimal expansion is irrational. Which of the following examples proves Rahul’s statement wrong?MediumLevel 15If (n) is a positive integer and (n) is not a perfect square, what type of number will (\sqrt{n}) be?MediumLevel 15Reema says that the sum of two irrational numbers is always irrational. Which of the following examples proves her statement wrong?MediumLevel 15Which statement is correct about (\sqrt{13}+\sqrt{17})?MediumLevel 15Which is the simplified form of √392?MediumLevel 15A student says, “Every non-terminating decimal expansion is irrational.” Which of the following examples proves this statement wrong?MediumLevel 15What is the result of (11\sqrt{3}-4\sqrt{3})?MediumLevel 15What is the value of (\sqrt{5}(\sqrt{45}+\sqrt{80}))?MediumLevel 15Reena says that the sum of two irrational numbers is always irrational. Which of the following examples correctly shows the error in her statement?MediumLevel 15Rina says, “The sum of two irrational numbers is always irrational.” What is the correct evaluation of her statement?MediumLevel 15Which is the rationalised form of (\frac{4}{\sqrt{5}+1})?MediumLevel 15A student says that every non-terminating decimal is irrational. Which example shows the error in this statement?MediumLevel 15What is the product of (10+\(\sqrt{29}\)) and (10-\(\sqrt{29}\))?MediumLevel 15