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 of the following is the value of \(3\sqrt{2}\times 2\sqrt{2}\)?EasyLevel 27If \(a=\sqrt{20}\), what is the simplified form of \(a\)?MediumLevel 25Which statement is correct for (3+\sqrt{7})?MediumLevel 25Which of the following is a non-terminating repeating decimal?MediumLevel 25Which number cannot be written in the form (\frac{p}{q}) where (q\neq0)?MediumLevel 25If \(x=\sqrt{11}\), what type of number is \(x^2+1\)?MediumLevel 25Which of the following gives the correct value of \(\sqrt{75}-\sqrt{27}\)?MediumLevel 25Which option is an example where the product of two irrational numbers is rational?MediumLevel 25Which decimal shows an irrational number?MediumLevel 25What is the simplified form of \((\sqrt{2}+\sqrt{8}+\sqrt{18})\)?MediumLevel 25Which option gives the correct relation between \(\sqrt{3}\) and \(\sqrt{12}\)?MediumLevel 25Which of the following is an irrational number between 6 and 7?MediumLevel 25If \(a=2-\sqrt{5}\) and \(b=2+\sqrt{5}\), what type of number is \(a+b\)?MediumLevel 25Which option gives the value of \(\sqrt{0.25}+\sqrt{0.04}\)?MediumLevel 25What is the value of \(\dfrac{\sqrt{45}}{\sqrt{5}}\)?MediumLevel 25If \(x = 0.\overline{12}\), what type of number is \(x\)?MediumLevel 25A student claims that the sum of two irrational numbers is always irrational. Which example proves the claim wrong?MediumLevel 25Reena says that \(0.101001000100001\ldots\) is rational because it contains only the digits 0 and 1. Which conclusion correctly identifies the error in her statement?MediumLevel 25If \(y=\sqrt{2}+\sqrt{32}\), what is the simplified form of \(y\)?MediumLevel 25Which statement is correct about the sum of two irrational numbers?MediumLevel 25