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 simplified surd form of \(\sqrt{320}\)?MediumLevel 3What is obtained by simplifying √363?EasyLevel 1What is the simplest form of \(\sqrt{432}\)?MediumLevel 3Ravi says that \(\frac{7}{24}\) is an irrational number because its decimal expansion is non-terminating. What is the error in Ravi's statement?MediumLevel 3A student says that \(0.101001000100001\ldots\) is a rational number because its decimal expansion contains only the digits 0 and 1. Which statement correctly explains the student's error?MediumLevel 3What is the value of ( \sqrt{7}(4+\sqrt{7}) )?MediumLevel 3Which of the following statements about decimal expansions is correct?MediumLevel 3What is the simplified form of (7 − √3)²?MediumLevel 3What is the value of \((6+\sqrt{23})(6-\sqrt{23})\)?MediumLevel 3A student says that \(\sqrt{2}+\sqrt{8}\) is an irrational number. Why is the statement correct?MediumLevel 3What is the rationalised form of ?MediumLevel 3What is the rationalised form of ( \frac{9}{4\sqrt{5}} )?MediumLevel 3What is the rationalised form of ( \frac{1}{\sqrt{13}+\sqrt{12}} )?MediumLevel 3What is the rationalised form of \(\frac{1}{\sqrt{17}-\sqrt{8}}\)?MediumLevel 3What is the simplified form of ( \sqrt{128}+\sqrt{200}-\sqrt{72} )?MediumLevel 3What is the simplified form of \(3\sqrt{54}+2\sqrt{150}\)?MediumLevel 3Which of the following numbers has a non-terminating, non-repeating decimal expansion and is therefore irrational?MediumLevel 3A student says that the decimal expansion of every irrational number is non-terminating and recurring. Why is this statement incorrect?MediumLevel 3What is the value of √45 × √80?MediumLevel 3What is the value of ( \sqrt{242}\div\sqrt{2} )?MediumLevel 3