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 gives the correct nature of (\sqrt{225}) and (\sqrt{226})?MediumLevel 25Which statement is correct about the number 0.2020020002...?MediumLevel 25If a number has a terminating or repeating decimal, what type of number will it be?MediumLevel 25Which of the following is the value of the product (1+\sqrt{3})(1-\sqrt{3})?MediumLevel 25Which option is the simplified form of (\sqrt{12}+\sqrt{75}-\sqrt{27})?MediumLevel 25Which option correctly describes the nature of \(\frac{1}{2}+\sqrt{2}\)?MediumLevel 25Which of the following is the simplified form of \(\sqrt{300}\)?MediumLevel 25If (x=4+\sqrt{7}) and (y=4-\sqrt{7}), what is the simplified form of (x-y)?MediumLevel 25Which of the following is the simplified form of \(\sqrt{180}\)?MediumLevel 26If \(x=\sqrt{17}\), what type of number is \(x^2-5\)?MediumLevel 26Which option correctly describes the nature of (4+\sqrt{13})?MediumLevel 26Which option is correct about (7-\sqrt{19})?MediumLevel 26Which of the following is the simplified form of (\sqrt{125}+\sqrt{45})?MediumLevel 26Which of the following is the simplified form of \(\sqrt{192}-\sqrt{27}\)?MediumLevel 26Which option is the value of (\sqrt{10}\times\sqrt{40})?MediumLevel 26Which option correctly describes the nature of (\sqrt{6}\times\sqrt{10})?MediumLevel 26If \(a=3+\sqrt{6}\) and \(b=3-\sqrt{6}\), what is the value of \(a+b\)?MediumLevel 26If (u=6+\sqrt{5}) and (v=6-\sqrt{5}), what is the value of (uv)?MediumLevel 26Which of the following is the value of \,((\sqrt{11}+2)(\sqrt{11}-2))\,?MediumLevel 26Which of the following is the correct expansion of \((3+\sqrt{2})^2\)?MediumLevel 26