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 that \(4+\sqrt{3}\) is rational because 4 is rational. What is the error in the student's conclusion?MediumLevel 14Which statement is correct about (\sqrt{5}+\sqrt{7})?MediumLevel 14What is the simplified value of \(\left(\frac{\sqrt{112}}{\sqrt{7}}\right)\)?MediumLevel 14What is the result of (8\sqrt{2}-5\sqrt{2})?MediumLevel 14What is the value of (\sqrt{2}(\sqrt{8}+\sqrt{18}))?MediumLevel 14Riya says, “The sum of two irrational numbers is always irrational.” Which of the following examples proves her statement wrong?MediumLevel 14What is the simplified form of √3 × (2√3 + 5)?MediumLevel 14Which is the rationalised form of (\frac{2}{\sqrt{3}+1})?MediumLevel 14What is the sum of \((8+\sqrt{17})\) and \((8-\sqrt{17})\)?MediumLevel 14A student says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which is the correct evaluation of this statement?MediumLevel 14If (q=5-\sqrt{2}), what type of number is (q)?MediumLevel 14To construct (\sqrt{5}) on the number line, which right triangle hypotenuse can be used?MediumLevel 14What is the value of \((\sqrt{54}\div\sqrt{6})\)?MediumLevel 14If the area of a square is (50) square units, what will be the simplified form of its side?MediumLevel 14What is the rationalised form of (\frac{1}{4-\sqrt{7}})?MediumLevel 14A student calls the number \(0.101001000100001\ldots\) rational because its decimal expansion is infinite. Which conclusion is correct?MediumLevel 14What is the simplified form of (3\sqrt{7}+2\sqrt{28})?MediumLevel 14Which option will have a non-terminating non-repeating decimal expansion?MediumLevel 14A student writes the number \(0.101001000100001\ldots\), in which the number of zeros between successive 1s keeps increasing. Which statement about this number is correct?MediumLevel 14Riya claims that every non-terminating decimal is irrational. Which of the following examples proves her claim wrong?MediumLevel 14