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
If r = 1/(√17 + 4), which is the simplified form of r?MediumLevel 15What is the value of ((\sqrt{27}+\sqrt{75})^2)?HardLevel 15What is the rationalised form of (\frac{3}{\sqrt{14}+\sqrt{5}})?HardLevel 15What is the value of (\frac{\sqrt{18}+\sqrt{72}}{\sqrt{2}})?HardLevel 15If (a=\sqrt{12}+\sqrt{75}) and (b=\sqrt{48}), what is the simplified form of (a-b)?HardLevel 15A student says that \(\sqrt{12}-\sqrt{3}\) is the difference of two square roots, so it is a rational number. Which is the correct correction of the student's error?HardLevel 15What is the rationalised form of (\frac{4}{\sqrt{13}-\sqrt{5}})?HardLevel 15If a rectangle has length (\sqrt{11}+\sqrt{6}) and breadth (\sqrt{11}-\sqrt{6}), what will be its area?HardLevel 15In which option is the product of two irrational numbers rational?HardLevel 15Which is the simplified form of (\frac{\sqrt{5}+2}{\sqrt{5}-2})?ExpertLevel 13A student says, “Every number with a non-terminating decimal expansion is irrational.” Which of the following numbers proves this statement wrong?ExpertLevel 13What is the simplified form of \(\sqrt{200}-\sqrt{72}+\sqrt{18}\)?ExpertLevel 13If r is a non-zero irrational number and q is a non-zero rational number, which of the following statements is always true?ExpertLevel 13Which of the following numbers, based on its decimal expansion, is irrational?ExpertLevel 13A student claims, “The sum of two irrational numbers is always irrational.” Which of the following examples proves this claim wrong?ExpertLevel 13What is the rationalised form of (\frac{3}{\sqrt{7}+\sqrt{4}})?ExpertLevel 13What is the value of (\sqrt{6+\sqrt{7}}\times\sqrt{6+\sqrt{7}})?ExpertLevel 13If \(x\) is an irrational number and \(r\) is a non-zero rational number, which statement about \(rx\) is always true?ExpertLevel 13Reema writes the number \(0.101001000100001\ldots\), in which the number of zeros between successive 1s keeps increasing. Which conclusion about this number is correct?ExpertLevel 13If \(x\) is an irrational number and \(r\) is a non-zero rational number, which of the following statements is always true?ExpertLevel 13