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Subjects

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 value of ( \sqrt{\frac{81}{121}}-\sqrt{\frac{4}{49}} )?MediumLevel 2Which option is an irrational number between (5) and (6)?MediumLevel 2Which number is greater: \(\sqrt{45}\) or \(\frac{13}{2}\)?MediumLevel 2Between which two integers does ( \sqrt{68} ) lie?MediumLevel 2Between which two integers does √86 lie?MediumLevel 2Which is greater between ( -\sqrt{50} ) and ( -7.2 )?MediumLevel 2If (0.070070007...) has no regular repetition, what is it?MediumLevel 2What is the correct statement about the decimal form of ( \frac{21}{80} )?MediumLevel 2A square tile has a side length of 1 cm. According to the Pythagorean theorem, its diagonal is \(\sqrt{2}\) cm. Which statement about this length is correct?MediumLevel 2A square has a side length of 5 cm. What type of number is the length of its diagonal?MediumLevel 2A student calls the number \(0.101001000100001\ldots\) rational because it contains only the digits 0 and 1. Which conclusion about this number is correct?MediumLevel 2A student considers the number \(0.101001000100001\ldots\) rational because its decimal expansion does not terminate. What is the correct conclusion about this number?MediumLevel 2What is the product of \(3+\sqrt{14}\) and \(3-\sqrt{14}\)?MediumLevel 2What is the value of (3 + √2)/(3 − √2) after rationalising?HardLevel 2What will be the denominator after rationalising ( \frac{\sqrt{7}+2}{\sqrt{7}-2} )?MediumLevel 2A student writes: \(\sqrt{2}+\sqrt{8}=\sqrt{10}\). Which is the correct evaluation of this statement?MediumLevel 2What is the value of \(\left|\sqrt{25}-\sqrt{100}\right|\)?MediumLevel 2What is the value of \(\sqrt{(-9)^2}\) in the real number system?MediumLevel 2If \(x=-8\), what is the value of \(\sqrt{x^2}+x\)?MediumLevel 2What is the rationalised form of ( \frac{1}{5+2\sqrt{6}} )?MediumLevel 2