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 number definitely lies between (\sqrt{10}) and (\sqrt{12})?HardLevel 14A student claims that \(\frac{\sqrt{18}}{\sqrt{2}}\) must be irrational because both the numerator and denominator are irrational. What is the correct conclusion?HardLevel 14What is the value of (\frac{\sqrt{125}-\sqrt{20}}{\sqrt{5}})?HardLevel 14What is the square of \(\sqrt{7+\sqrt{10}}\) equal to?HardLevel 14If \(p\) is an irrational number and \(q\) is a non-zero rational number, which of the following statements is always true?HardLevel 14In which option is the difference of two irrational numbers rational?HardLevel 14What is the value of (√20 + √45)(√20 − √45)?MediumLevel 14Which of the following statements is always true about the sum of two irrational numbers?HardLevel 14Which is the simplified form of (\frac{\sqrt{7}+\sqrt{3}}{\sqrt{7}-\sqrt{3}})?HardLevel 14A student claims that \(5-\sqrt{7}\) is a rational number. Which argument correctly proves that the claim is wrong?HardLevel 14What is the simplified form of (\sqrt{245}-\sqrt{180}+\sqrt{80})?HardLevel 14If r = 1/(√11 + 3), which is the simplified form of r?MediumLevel 14What is the value of ((\sqrt{18}+\sqrt{50})^2)?HardLevel 14What is the rationalised form of (\frac{2}{\sqrt{11}+\sqrt{7}})?HardLevel 14If (s=\sqrt{98}+\sqrt{200}), what is the value of (\frac{s}{\sqrt{2}})?HardLevel 14If a = √3 + √5 and b = √5 − √3, what is the value of ab?MediumLevel 14Which option will remain irrational?HardLevel 14Which conclusion about the side of a square tile with an area of 50 cm² is correct?HardLevel 14What is the value of (√45 + √5)(√45 − √5)?MediumLevel 14A student claims, “The sum of two irrational numbers is always irrational.” Which of the following pairs disproves this claim?HardLevel 15