Mathematics
Real Numbers
वास्तविक संख्याएँ
Real Numbers is a Class 9 Mathematics topic in the Number Systems chapter. Students learn how rational and irrational numbers together form the real number system, represent them on the number line, and distinguish between their decimal expansions. The topic develops understanding of terminating and non-terminating decimals, recurring and non-recurring forms, and the key properties of real numbers under addition, subtraction, multiplication, and division. It also builds a foundation for working confidently with numbers in algebra and geometry.
Practice questions
What is the simplest form of \(\sqrt{288}\)?MediumLevel 2What is the simplified form of \(2\sqrt{45}+3\sqrt{20}\)?MediumLevel 2What is the simplified form of \(4\sqrt{27}-2\sqrt{75}\)?MediumLevel 2What is the value of ( \sqrt{5}(3+\sqrt{5}) )?MediumLevel 2What is the expansion of \((4+\sqrt{3})^2\)?MediumLevel 2What is the simplified form of ( (6-\sqrt{8})^2 )?MediumLevel 2What is the value of the expression \((5+\sqrt{17})(5-\sqrt{17})\)?MediumLevel 2A student simplifies \\(\sqrt{50}\\) as \\(5\sqrt{2}\\) and calls it an irrational number. Which evaluation of the student's conclusion is correct?MediumLevel 2What is the rationalised form of ( \frac{5}{3\sqrt{2}} )?MediumLevel 2What is the rationalised form of 1/(√10 + √9)?MediumLevel 4What is the rationalised form of \(\frac{1}{\sqrt{11}-\sqrt{2}}\)?MediumLevel 2What is the simplified form of ( \sqrt{98}+\sqrt{162}-\sqrt{50} )?MediumLevel 2What is the simplified form of \(2\sqrt{44}+3\sqrt{99}\)?MediumLevel 2What is the simplified form of (\sqrt{112}+2\sqrt{175})?MediumLevel 2What is the simplified form of \(5\sqrt{48}-3\sqrt{75}\)?MediumLevel 2What is the value of √32 × √50?MediumLevel 2What is the value of ( \sqrt{180}\div\sqrt{20} )?MediumLevel 2What is the value of \(\frac{\sqrt{200}}{\sqrt{2}}+\sqrt{16}\)?MediumLevel 2What is the value of (\sqrt{4.84}-\sqrt{1.44})?MediumLevel 2What is the value of ( \sqrt{\frac{16}{25}}+\sqrt{\frac{9}{64}} )?MediumLevel 2