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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 of the following is the value of \((\sqrt{5}+\sqrt{2})(\sqrt{5}-\sqrt{2})\)?MediumLevel 27 Which of the following is the simplified form of (2\sqrt{3} + \sqrt{12})?MediumLevel 27 Which option represents a rational number?MediumLevel 27 If x = \sqrt{23}, what type of number is x^2 + 2x?MediumLevel 27 Which of the following is the value of \( (\sqrt{3}+\sqrt{12})^2 \)?MediumLevel 27 Which of the following is an irrational number between 9 and 10?MediumLevel 27 Which of the following is a rational number between 6 and 7?MediumLevel 27 Which of the following correctly lists the two consecutive integers between which \(\sqrt{11}\) lies?MediumLevel 27 Which option correctly compares (\sqrt{130}) and (\sqrt{145})?MediumLevel 27 Which option is the value of (\sqrt{0.36}+\sqrt{0.49})?MediumLevel 27 Which of the following is the value of \(\frac{\sqrt{147}}{\sqrt{3}}\)?MediumLevel 27 Which option is the simplified form of (4/√2)?MediumLevel 27 Which statement is correct for (\sqrt{a}) when (a) is a positive integer?MediumLevel 27 Which of the following equals \(\sqrt{2}(5-\sqrt{2})\)?MediumLevel 27 What is the value of the expression \((3\sqrt{6}\times2\sqrt{6})\)?MediumLevel 27 Which of the following is the simplified form of (6\sqrt{3}-2\sqrt{3}+\sqrt{3})?MediumLevel 27 Which option is the simplified form of (\sqrt{75}+\sqrt{108}-\sqrt{48})?MediumLevel 27 Which option is the simplified form of (\sqrt{27}+\sqrt{75}-\sqrt{12})?MediumLevel 27 Which of the following correctly describes the type of the number \(0.\overline{09}\)?MediumLevel 27 Which of the following statements is true about the decimal number \(8.01011011101111\ldots\)? (Observe the pattern of digits after the decimal point)MediumLevel 27