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 claims that \(\frac{1}{\sqrt{5}+2}\) is a rational number because its numerator is 1. Which is the correct evaluation of this claim?HardLevel 13Which number definitely lies between (\sqrt{6}) and (\sqrt{7})?HardLevel 13Let p and q be rational numbers with q ≠ 0. If a student claims that \(\frac{p+\sqrt{2}}{q}\) is rational, which conclusion would follow from the claim?HardLevel 13What is the value of (\frac{\sqrt{45}-\sqrt{20}}{\sqrt{5}})?HardLevel 13What is the square of \(\sqrt{2+\sqrt{3}}\) equal to?HardLevel 13Which of the following decimal representations denotes an irrational number?HardLevel 13Let \(x\) be an irrational number and \(r\) be a rational number. Which of the following statements is always true?HardLevel 13What is the value of (√8 + √18)(√8 − √18)?MediumLevel 13Riya claims that the product of any two irrational numbers is always irrational. Which of the following pairs is a counterexample to her claim?HardLevel 13Which of the following statements is always true, where a rational number may also be zero?HardLevel 14Which is the simplified form of (\frac{3+\sqrt{2}}{3-\sqrt{2}})?HardLevel 14A student says that the product of any two irrational numbers is always irrational. Which option correctly evaluates this statement using
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?HardLevel 14What is (\sqrt{108}-\sqrt{48}+\sqrt{12}) equal to?HardLevel 14If (p=\frac{1}{\sqrt{7}+2}), which is the simplified form of (p)?HardLevel 14What is the value of (\sqrt{5+\sqrt{6}}\times\sqrt{5+\sqrt{6}})?HardLevel 14A student claims that the number 0.101001000100001... is rational because it contains only the digits 0 and 1. What is the correct evaluation of this claim?HardLevel 14What is the simplified form of (\frac{\sqrt{3}+1}{\sqrt{3}-1})?HardLevel 14If x = √5 + √2 and y = √5 − √2, what is the value of x/y?MediumLevel 14If \(x\) is an irrational number and \(r\) is a rational number, which of the following will always be irrational?HardLevel 14Which statement is definitely true about (\sqrt{8+\sqrt{15}})?HardLevel 14