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 \((x=\sqrt{7}+3)\), what type of number is \((x-3)\)?MediumLevel 14Which is the simplified form of (\sqrt{32}+\sqrt{18})?MediumLevel 14A student says that the product of a non-zero rational number and an irrational number is always irrational. Which is the best reason why the statement is correct?MediumLevel 14A student says that the sum of two irrational numbers is always irrational. Which example proves the statement false?MediumLevel 14For a natural number \(n\), what is the correct criterion for \(\sqrt{n}\) to be irrational?MediumLevel 14Ravi said, “If the decimal expansion of a number is non-terminating, then it must be irrational.” What is the flaw in Ravi’s statement?MediumLevel 14Which is the simplified form of (\sqrt{75}-\sqrt{12})?MediumLevel 14What type of number is the decimal (2.303003000300003\ldots)?MediumLevel 14A student claims, “The sum of any two irrational numbers is always irrational.” Which example proves the claim wrong?MediumLevel 14Which is the simplified form of (\sqrt{80}+\sqrt{125})?MediumLevel 14Which number lies between (\sqrt{15}) and (\sqrt{20})?MediumLevel 14A student says that \(0.101001000100001\ldots\) is rational because the digit 1 occurs repeatedly. Which conclusion is correct?MediumLevel 14Which option is an example of an irrational number?MediumLevel 14Reema says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which is the correct evaluation of her statement?MediumLevel 14What is the rationalised form of (\frac{3}{\sqrt{7}})?MediumLevel 14Which of the following statements about irrational numbers is always true?MediumLevel 14What is the irrational part in \((6-\sqrt{10})\)?MediumLevel 14What is the simplified form of (\sqrt{45}+\sqrt{125}-\sqrt{20})?MediumLevel 14A student says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. What is the correct correction to the student’s error?MediumLevel 14If (n) is a positive integer and (n) is a perfect square, what type of number will (\sqrt{n}) be?MediumLevel 14