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
What type of number is \(\sqrt{7}\times\sqrt{14}\)?MediumLevel 1What is the rationalised form of \(\frac{6}{\sqrt{7}}\)?MediumLevel 2What type of number is \(\sqrt{3}\times\sqrt{21}\)?MediumLevel 2If 0.01001000100001... is non-terminating and non-repeating, what type of number is it?MediumLevel 1What is the simplified form of √2 + √8 + √18?MediumLevel 1If \(0.12112211122211112222\ldots\) is non-terminating and non-repeating, what type of number is it?EasyLevel 2What is the value of (1/(3+√8)+1/(3−√8))?HardLevel 2(3+√2) belongs to which set?MediumLevel 3(1-\sqrt{3}) is what type of number?HardLevel 3If (x=\sqrt{11}) then (x) isHardLevel 3Which pair is both irrational?HardLevel 3Which number is not rational?HardLevel 3If (a) is rational and (b) is irrational then (a+b) is generally?HardLevel 3Which decimal represents an irrational number?HardLevel 3If (a=\sqrt{2}) then (a+\frac{1}{a}) is what type of number?HardLevel 3Which of the following is irrational?ExpertLevel 1If (x=\sqrt{7}) then (x+\frac{1}{x}) is what type of number?ExpertLevel 1Which decimal expansion represents an irrational number?ExpertLevel 1If (x=\sqrt{13}) then what type of number is (x)?ExpertLevel 1If (\sqrt{7}) is irrational then (3\sqrt{7}) is?ExpertLevel 2