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 number is an irrational number?EasyLevel 25Which number is a rational number?EasyLevel 25All rational and irrational numbers together form which set?EasyLevel 25What type of number is the decimal 0.333...?EasyLevel 25The decimal \(0.1010010001\ldots\) that shows no fixed repeating block is what type of number?EasyLevel 25What type of number is \(\sqrt{49}\)?EasyLevel 25Which statement is correct about √11?EasyLevel 25Which is the correct definition of a rational number?EasyLevel 25What is the decimal expansion of an irrational number like?EasyLevel 25What type of number is \(\pi\)?EasyLevel 25What type of number is 0?EasyLevel 25What type of number is (2+\sqrt{3})?EasyLevel 25What is the simplest form of \(\sqrt{2}+\sqrt{2}\)?EasyLevel 25What is the simplified form of \(\sqrt{18}\)?EasyLevel 25Which number is not a real number?EasyLevel 25What type of number is 1.25?EasyLevel 25Which of the following decimals represents a rational number?EasyLevel 25Reena says, “Every non-terminating decimal is irrational.” What is the error in her statement?EasyLevel 25If a is rational and b is irrational, when is a + b definitely irrational?EasyLevel 25What is the simplified form of \(\sqrt{12}\)?EasyLevel 25