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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 a rational number between 7 and 8?MediumLevel 26 Which option correctly gives the two nearest integers between which \(\sqrt{7}\) lies?MediumLevel 26 Which of the following comparisons between \(\sqrt{90}\) and \(\sqrt{99}\) is correct?MediumLevel 26 Which of the following is the value of \(\sqrt{0.64}+\sqrt{0.09}\)?MediumLevel 26 Which of the following is the value of \\(\frac{\sqrt{80}}{\sqrt{5}}\\)?MediumLevel 26 Which option is the simplified form of (\frac{3}{\sqrt{3}})?MediumLevel 26 Which of the following is the value of \(\sqrt{3}(4+\sqrt{3})\)?MediumLevel 26 What is the value of \(2\sqrt{5}\times 3\sqrt{5}\)?MediumLevel 26 Which of the following is the simplified form of \\(5\sqrt{2}+3\sqrt{2}-\sqrt{2}\\)?MediumLevel 26 Which option is the simplified form of (\sqrt{50}+\sqrt{72}-\sqrt{32})?MediumLevel 26 Which option is the correct simplified form of (\sqrt{200})?MediumLevel 26 Which option correctly describes the nature of (0.\overline{123})?MediumLevel 26 Which statement is correct about the decimal number 3.010010001...?MediumLevel 26 If (m) is a positive integer and (\sqrt{m}) is rational, what must (m) be?MediumLevel 26 If (\sqrt{k}) is irrational and (k) is a positive integer, what is correct about (k)?MediumLevel 26 Which option gives the correct nature of (\sqrt{289}) and (\sqrt{290})?MediumLevel 26 Which option correctly describes the numerical nature of \(\sqrt[3]{125}\)?MediumLevel 26 Which of the following statements about \(\sqrt[3]{12}\) is correct?MediumLevel 26 Which option makes (2+\sqrt{m}) irrational?MediumLevel 26 Which option makes (9-\sqrt{m}) rational?MediumLevel 26