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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 option is both a natural number and a rational number?EasyLevel 27 If (n) is a positive integer and (\sqrt{n}) is irrational then what can be said about (n)?EasyLevel 27 Which of the following is the value of \(\sqrt{0.16}\)?EasyLevel 27 Which of the following numbers is real but irrational?EasyLevel 27 Which option is formed by adding a rational number to an irrational number?EasyLevel 27 Which option gives the simplified form of \(\sqrt{150}\)?EasyLevel 27 Which option is the simplified form of (\sqrt{200})?EasyLevel 27 What is the simplified form of \(\sqrt{2}+\sqrt{18}\)?EasyLevel 27 What is the simplified form of \(\sqrt{3}+\sqrt{75}\)?EasyLevel 27 Which of the following statements about zero (0) is correct?EasyLevel 27 Which of the following correctly describes \(0.123456789101112\ldots\)?EasyLevel 27 Which option is a set of only rational numbers?EasyLevel 27 Which option is a set of only irrational numbers?EasyLevel 27 If \(p\) and \(q\) are integers and \(q \neq 0\), what is a number of the form \(\frac{p}{q}\) called?EasyLevel 27 If a number is not rational but is real, what is it called?EasyLevel 27 Which of the following statements about \(3-\sqrt{11}\) is correct?EasyLevel 27 Which option gives the correct nature of (\sqrt{256}) and (\sqrt{257})?EasyLevel 27 Which of the following is the simplified form of \(\sqrt{242}\)?EasyLevel 27 What type of number is the value of the expression \((5+\sqrt{7})-(2+\sqrt{7})\)?EasyLevel 27 Which of the following is the correct simplified form of \(7\sqrt{3}+2\sqrt{3}\)?EasyLevel 27