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 (\frac{2+\sqrt{3}}{2-\sqrt{3}})?HardLevel 13If \(x\) is an irrational number, which of the following numbers will always be irrational?HardLevel 13What is (\sqrt{45}+\sqrt{20}-\sqrt{80}) equal to?HardLevel 13A student claims that the sum of two irrational numbers is always irrational. Which example shows the error in this claim?HardLevel 13How can (\sqrt{3+\sqrt{5}}) be identified according to the given statements?HardLevel 13If m = √8 + √18 and n = √50, what is the value of m − n?MediumLevel 13If x = 1/(√2 + 1), what is the value of x + √2?MediumLevel 13A student examines the number \(x=0.101001000100001\ldots\) and draws a conclusion about its type. Which of the following conclusions is correct?HardLevel 13Which of the following expressions can be rational for an irrational number \(x\)?HardLevel 13If \(x\) is an irrational number, which of the following expressions will always be a rational number?HardLevel 13What is the simplified form of (\sqrt{48}+\sqrt{75}-\sqrt{27})?HardLevel 13What is the value of (\frac{\sqrt{72}+\sqrt{50}}{\sqrt{2}})?HardLevel 13If \(x\) is an irrational number, which of the following statements is not necessarily true?HardLevel 13What is the value of ((\sqrt{5}+\sqrt{2})^2-(\sqrt{5}-\sqrt{2})^2)?HardLevel 13What is the simplified form of (\frac{3+\sqrt{5}}{3-\sqrt{5}})?HardLevel 13If (x=\sqrt{3}+\sqrt{2}) and (y=\sqrt{3}-\sqrt{2}), what is the value of (\frac{x}{y})?HardLevel 13Which option has an irrational value?HardLevel 13A student says, “The product of any two irrational numbers is always irrational.” Which is the correct evaluation of the statement?HardLevel 13Which statement is definitely true about (\sqrt{6+\sqrt{11}})?HardLevel 13If u = √80 − √45 and v = √5, what is the value of u + v?MediumLevel 13