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 (\sqrt{50}-\sqrt{2})?MediumLevel 13What is the simplified form of (\sqrt{3}+\sqrt{12}+\sqrt{27})?MediumLevel 13What type of number does decimal (1.02002000200002\ldots) represent?MediumLevel 13What is the value of \(\left(\frac{\sqrt{27}}{\sqrt{3}}\right)\)?MediumLevel 13Which is the simplified form of (\sqrt{45}+\sqrt{20})?MediumLevel 13Which number lies between √2 and √8?MediumLevel 13The area of a square garden is \(18\,\text{m}^2\). Which conclusion about the length of its side is correct?MediumLevel 13Which option represents an irrational number?MediumLevel 13Riya says that \(0.1010010001\ldots\) is a rational number because it contains only the digits 0 and 1. What is the correct evaluation of Riya’s statement?MediumLevel 13A student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. What is the student's error?MediumLevel 13What is the irrational part of (4 + √6)?MediumLevel 13What is the simplified form of (\sqrt{28}+\sqrt{63}-\sqrt{7})?MediumLevel 13A student says, “Every non-terminating decimal is irrational.” Which of the following examples proves the statement wrong?MediumLevel 13If (n) is not a perfect square and (n>0), what type of number will (\sqrt{n}) generally be?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 conclusion?MediumLevel 13Which statement is correct about (\sqrt{2}+\sqrt{3})?MediumLevel 13A student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. Which conclusion is correct?MediumLevel 13Which option is a non-terminating and repeating decimal?MediumLevel 13Nikhil claims that every non-terminating decimal expansion is irrational. Which of the following numbers shows the error in his claim?MediumLevel 13What is the value of \(\sqrt{3}(\sqrt{3}+\sqrt{12})\)?MediumLevel 13