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 statement is correct about the product of two irrational numbers?MediumLevel 25Which of the following is the value of \(\sqrt{5}(2+\sqrt{5})\)?MediumLevel 25Which of the following is the value of \((\sqrt{7}+1)(\sqrt{7}-1)\)?MediumLevel 25Which of the following is the correct expansion of \\((2+\sqrt{3})^2\\)?MediumLevel 25Which of the following numbers lies between 3 and 4 and is irrational?MediumLevel 25Which option is an irrational number between (0) and (1)?MediumLevel 25If (\sqrt{n}) is rational and (n) is a positive integer, what is correct about (n)?MediumLevel 25Which of the following correctly describes the nature of \(2.\overline{45}\)?MediumLevel 25Which of the following is the simplified form of \(\sqrt{162}\)?MediumLevel 25Which of the following is the value of \(4\sqrt{3}-\sqrt{27}\)?MediumLevel 25Which of the following is the simplified form of \(\sqrt{5}+\sqrt{20}-\sqrt{45}\)?MediumLevel 25Which of the following is the simplified form of \(\frac{2}{\sqrt{2}}\)?MediumLevel 25If \(a=\sqrt{6}+1\), what type of number is \(a-1\)?MediumLevel 25Which option correctly gives the two nearest integers between which \(\sqrt{2}\) lies?MediumLevel 25Which option correctly compares (\sqrt{50}) and (\sqrt{72})?MediumLevel 25Which of the following is the value of \(\sqrt{0.81}\)?MediumLevel 25If u = 5 + \sqrt{2} and v = 5 - \sqrt{2}, what is the value of uv?MediumLevel 25Which option correctly describes the nature of \(\sqrt[3]{64}\)?MediumLevel 25Which of the following is true for (\sqrt[3]{16})?MediumLevel 25If (2+\sqrt{m}) is irrational and (m) is a positive integer, which (m) can be correct?MediumLevel 25