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{4+\sqrt{7}}{4-\sqrt{7}})?HardLevel 15A student says that every non-terminating decimal number is irrational. Which of the following numbers shows the error in this statement?HardLevel 15What is (\sqrt{147}-\sqrt{75}+\sqrt{27}) equal to?HardLevel 15If (p=\frac{1}{\sqrt{13}+3}), which is the simplified form of (p)?HardLevel 15What is the value of (\sqrt{9+\sqrt{20}}\times\sqrt{9+\sqrt{20}})?HardLevel 15If two irrational numbers \(a\) and \(b\) are such that \(a+b\) is rational, which conclusion about \(ab\) is correct?HardLevel 15What is the simplified form of (\frac{\sqrt{5}+2}{\sqrt{5}-2})?HardLevel 15If (x=\sqrt{8}+\sqrt{3}) and (y=\sqrt{8}-\sqrt{3}), what is the value of (\frac{x}{y})?HardLevel 15If \(a\) is an irrational number and \(b\) is a non-zero rational number, which statement about \(a+b\) is always true?HardLevel 15Which statement is definitely true about (\sqrt{10+\sqrt{21}})?HardLevel 15If \(x\) is an irrational number and \(r\ne 0\) is a rational number, which of the following statements is always true?HardLevel 15Which is the rationalised form of (\frac{6}{\sqrt{15}-\sqrt{6}})?HardLevel 15What is the value of ((\sqrt{50}+\sqrt{98})^2)?HardLevel 15Which condition on two irrational numbers guarantees that their sum is rational?HardLevel 15What is the value of \(\sqrt{5}\left(\sqrt{125}-\sqrt{45}\right)\)?HardLevel 15What is the rationalised form of (\frac{5}{\sqrt{12}+\sqrt{7}})?HardLevel 15Which of the following statements correctly describes the relationship between rational and irrational numbers?HardLevel 15What is the value of (√(6 + √5) × √(6 + √5))?MediumLevel 15Which is the simplified form of (\sqrt{242}+\sqrt{128}-\sqrt{72})?HardLevel 15If (t=\sqrt{13}+3), what is the value of (t+\frac{4}{t})?HardLevel 15