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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

What is the product of (1+\sqrt{7}) and (1-\sqrt{7})?MediumLevel 26 Which option is the simplified form of (\sqrt{48}+\sqrt{108}-\sqrt{12})?MediumLevel 26 Which option correctly gives the sum and product of (2+√3) and (2−√3)?MediumLevel 26 Which option is the correct expansion of \((\sqrt{5}-\sqrt{2})^2\)?MediumLevel 26 If a decimal is terminating or repeating, what type of number is it?MediumLevel 26 Which option correctly describes the nature of \(\frac{1}{3}+\sqrt{11}\)?MediumLevel 26 Which of the following is the value of \(4\sqrt{7}-\sqrt{112}\)?MediumLevel 26 Which of the following is the simplified form of \(\sqrt{245}\)?MediumLevel 26 Which option is the value of ((4+\sqrt{7})(4-\sqrt{7}))?MediumLevel 26 Which option is the simplified form of (\sqrt{72}+\sqrt{128}-\sqrt{50})?MediumLevel 26 Which option is an irrational number between (8) and (9)?MediumLevel 26 If (x=2+\sqrt{10}) and (y=2-\sqrt{10}), what is the simplified form of (x-y)?MediumLevel 26 Which option is the value of \((\sqrt{13}-\sqrt{3})(\sqrt{13}+\sqrt{3})\)?MediumLevel 26 Which option is the correct expansion of \( (\sqrt{6}+\sqrt{2})^2 \)?MediumLevel 26 Which option correctly describes the nature of \(\sqrt[3]{216}\)?MediumLevel 26 Which option makes (5+\sqrt{m}) rational?MediumLevel 26 Which of the following is the simplified form of \(\sqrt{288}\)?MediumLevel 27 Which option is the simplified form of (√7+√63)?MediumLevel 27 Which of the following is the simplified form of \(\sqrt{98}-\sqrt{8}\)?MediumLevel 27 Which option is the value of (\sqrt{18}\times\sqrt{50})?MediumLevel 27