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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{49}{100}}-\sqrt{\frac{4}{25}} )?MediumLevel 1Which option is an irrational number between (2) and (3)?MediumLevel 1A student claims that the product of any two irrational numbers is always irrational. Which pair of numbers disproves this claim?MediumLevel 1Between which two integers does ( \sqrt{26} ) lie?MediumLevel 1Which is greater between ( -\sqrt{20} ) and ( -4.4 )?MediumLevel 1Which option is incorrect?MediumLevel 1A square has a side of \(\sqrt{2}\) cm. Which statement about its diagonal and perimeter is correct?MediumLevel 1What is the correct statement about the decimal form of ( \frac{13}{40} )?MediumLevel 1A student says, “\(\sqrt{18}\) is a rational number because 18 is an integer.” Which is the correct evaluation of this statement?MediumLevel 1What type of number is \(\sqrt{5}\times\sqrt{20}\)?MediumLevel 1What is the product of (2+\sqrt{13}) and (2-\sqrt{13})?MediumLevel 1What is the value of (2 + √3)/(2 − √3) after rationalising?HardLevel 2What will be the denominator after rationalising ( \frac{\sqrt{5}-1}{\sqrt{5}+1} )?MediumLevel 1A student says that \(0.101001000100001\ldots\) is a rational number because it contains only the digits 0 and 1. Which statement correctly explains the student's error?MediumLevel 1A student calls the number 0.101001000100001... rational because its decimal expansion is infinite. What should the correct conclusion be?MediumLevel 1What is the value of ( \sqrt{a^2} ) in real numbers?MediumLevel 1If \(x=-5\), what is the value of \(\sqrt{x^2}\)?MediumLevel 1What is the rationalised form of ( \frac{1}{\sqrt{3}+\sqrt{2}} )?MediumLevel 1What is the simplest surd form of \(\sqrt{180}\)?MediumLevel 2What is obtained by simplifying \(\sqrt{245}\)?MediumLevel 2