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
Which statement about the decimal number 9.0202202220... is correct?MediumLevel 27If (p=7+\sqrt{11}) and (q=7-\sqrt{11}), what is the value of (pq)?MediumLevel 27If (x=\sqrt{5}+\sqrt{2}), what type of number is (x^2-2\sqrt{10})?MediumLevel 25If (a=3+\sqrt{7}) and (b=3-\sqrt{7}), what is the value of (a^2+b^2)?HardLevel 25Which option is the value of ((\sqrt{11}+\sqrt{5})^2-(\sqrt{11}-\sqrt{5})^2)?HardLevel 25If (y=\sqrt{18}+\sqrt{50}-\sqrt{8}), what is the value of (y^2)?HardLevel 25Which option is the rationalized form of (1/(3+√5))?MediumLevel 25Which option is the simplified form of (\frac{2}{\sqrt{7}-\sqrt{3}})?HardLevel 25If (p=2+\sqrt{3}), what is (\frac{1}{p}) equal to?HardLevel 25Which option correctly describes the nature of ((5+\sqrt{6})(5-\sqrt{6})+\sqrt{24})?HardLevel 25If \(r=\sqrt{2}+\sqrt{3}\), what is the simplified form of \(r+\dfrac{1}{r}\)?HardLevel 25Which of the following is the simplified form of \(2\sqrt{12}-3\sqrt{27}+\sqrt{75}\)?HardLevel 25If (a=\sqrt{8}+\sqrt{18}), what type of number is (a^2)?HardLevel 25Which option correctly describes the nature of the expression (\sqrt{45}+\sqrt{80}-\sqrt{125})?HardLevel 25Which option definitely describes the nature of (\sqrt{3+\sqrt{5}})?HardLevel 25If \(x=\sqrt{6}-\sqrt{2}\), what is the simplified form of \(x^2\)?HardLevel 25Which option is the value of ((\sqrt{13}+\sqrt{12})(\sqrt{13}-\sqrt{12}))?HardLevel 25If (m=\frac{1}{\sqrt{5}+\sqrt{2}}), what is the simplified form of (m)?HardLevel 25Which option is the value of (\frac{\sqrt{27}+\sqrt{12}}{\sqrt{3}})?HardLevel 25Which option is a correct quadratic equation for (x=\sqrt{2}+\sqrt{3})?HardLevel 25