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 (q=7-\sqrt{11}), what type of number is (q)?MediumLevel 15To construct (\sqrt{10}) on the number line, which right triangle hypotenuse can be used?MediumLevel 15What type of number is (\sqrt{6}\times\sqrt{24})?MediumLevel 15A student says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which conclusion about this statement is correct?MediumLevel 15If the area of a square is (72) square units, what will be the simplified form of its side?MediumLevel 15What is the rationalised form of 1/(6 − √5)?MediumLevel 15Which statement is correct about (\sqrt{8}+\sqrt{200}) and (12\sqrt{2})?MediumLevel 15What is the simplified form of (4\sqrt{11}+3\sqrt{44})?MediumLevel 15A student says that every non-terminating decimal expansion is irrational. Which of the following numbers disproves the statement?MediumLevel 15A student claims that every non-terminating decimal number is irrational. Which of the following numbers is a counterexample to the claim?MediumLevel 15A student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. Which statement correctly corrects the student's claim?MediumLevel 15If x = √12 + 2√3, what is the simplified form of x?EasyLevel 15Rina says, “\(\sqrt{18}\) is rational because 18 is an integer.” Which option correctly identifies her error?MediumLevel 15Which is the rationalised form of (\frac{4}{\sqrt{3}+1})?MediumLevel 15If a = √8 − √2, what is a equal to?EasyLevel 15Which is irrational between (0.414141\ldots) and (0.4141141114\ldots)?MediumLevel 15What is the simplified value of (\frac{\sqrt{98}-\sqrt{18}}{\sqrt{2}})?MediumLevel 15Which of the following numbers has a decimal expansion that indicates it is an irrational number?MediumLevel 15A student says that the decimal number \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which statement correctly identifies the student's error?MediumLevel 15A student says, “The sum of two irrational numbers can never be rational.” Which of the following pairs proves this statement wrong?HardLevel 13