Mathematics
Irrational numbers and real numbers
अपरिमेय संख्याएँ और वास्तविक संख्याएँ
In this Class 10 Mathematics topic, students build a clear understanding of real numbers as the collection of rational and irrational numbers. They learn to identify irrational numbers, compare and represent real numbers on the number line, and interpret terminating, recurring, and non-terminating non-recurring decimals. The topic also develops confidence with properties and operations involving real numbers, providing useful foundations for reading polynomial expressions, coefficients, and real zeros in the surrounding Polynomials chapter.
Practice questions
If (x=2+√3), which equation is true?MediumLevel 25Which option is the value of (4√3+3√12−2√75)?EasyLevel 25Which option is a number between (\sqrt{2}) and (\sqrt{3})?HardLevel 25Which option is a rational number satisfying √50 < x < √72?MediumLevel 25Which option is the ascending order of (√48), (√75), (√108)?EasyLevel 25Which of the following is the value of \\(\sqrt{0.49}+\frac{1}{\sqrt{25}})\\?HardLevel 25If (n) is a positive integer and (\sqrt{n}) is irrational, when will (\sqrt{4n}) be rational?HardLevel 25Which option shows that (\sqrt{2}+\sqrt{8}) is irrational?HardLevel 25Which option is the value of (\frac{\sqrt{98}-\sqrt{18}}{\sqrt{2}})?HardLevel 25Which option is the simplified form of \(\left(\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}\right)\)?HardLevel 25If (a=\sqrt{5}+\sqrt{3}) and (b=\sqrt{5}-\sqrt{3}), what is the simplified form of (\frac{a}{b})?HardLevel 25Which of the following is the simplified form of (\sqrt{12}+\sqrt{27}+\sqrt{75}-\sqrt{48})?HardLevel 25Which of the following correctly describes the nature of the number \(0.101001000100001\ldots\)?HardLevel 25If (\sqrt{m}=a), where (a) is rational and (m) is a positive integer, what is necessary for (m)?HardLevel 25Which option describes the nature of (\sqrt{289}+\sqrt{290})?HardLevel 25Which of the following is the value of \(\sqrt[3]{216}+\sqrt[3]{125}\)?HardLevel 25If \(z=\sqrt[3]{9}\), what type of number is \(z^3\)?HardLevel 25Which option makes (8-\sqrt{m}) irrational?HardLevel 25Which option is the simplified form of ((\sqrt{2}+\sqrt{5}+\sqrt{8}))?HardLevel 25What is the value of \((\sqrt{20}-\sqrt{5})^2\)?HardLevel 25