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
What type of number is the value of \(\sqrt{0.04}\)?EasyLevel 25Which positive number has square equal to 2 and is irrational?EasyLevel 25What type of number is (7-\sqrt{2})?EasyLevel 25Which conclusion is correct if (n) is not a perfect square in the number (\sqrt{n})?EasyLevel 25Which option shows the correct simplified form of \(\sqrt{50}\)?EasyLevel 25Which option is an example of the product of a rational and an irrational number that is irrational?EasyLevel 25If \(x=2+\sqrt{5}\), what type of number is \(x-2\)?EasyLevel 25What is the simplified form of \(\sqrt{98}\)?EasyLevel 25Which statement is correct if a decimal is terminating?EasyLevel 25Which number is an example of an irrational number?EasyLevel 26A student says that \(0.272727\ldots\) is irrational because its decimal expansion is non-terminating. Which statement correctly explains the student's error?EasyLevel 26If the decimal expansion of a number terminates, what type of number is it?EasyLevel 26What type of number is the decimal 3.272727...?EasyLevel 26The decimal 5.123123312333... shows no fixed repeating pattern. What type of number is it?EasyLevel 26What type of number is the value of \(\sqrt{121}\)?EasyLevel 26Which statement is correct about (\sqrt{37})?EasyLevel 26Which option shows only rational numbers?EasyLevel 26Which statement about real numbers is correct?EasyLevel 26What type of number is (-8)?EasyLevel 26What type of number is (6+\sqrt{11})?EasyLevel 26