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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 \(\left|\sqrt{36}-\sqrt{121}\right|\)?MediumLevel 3What is the value of \(\sqrt{(-12)^2}\)?MediumLevel 3If \(x=-15\), what is the value of \(\sqrt{x^2}-x\)?MediumLevel 3What is the rationalised form of ( \frac{1}{6+\sqrt{35}} )?MediumLevel 3What is the simplified form of ( \sqrt{500}-\sqrt{180}+\sqrt{45} )?MediumLevel 3What is the simplified form of (2\sqrt{147}-3\sqrt{75}+\sqrt{300})?HardLevel 1Choose the correct simplified form of (4\sqrt{72}+2\sqrt{200}-5\sqrt{50}).HardLevel 1What is the value of ( \sqrt{18}(2\sqrt{8}-\sqrt{50}) )?HardLevel 1A student says that the decimal expansion of \(\frac{77}{480}\) will terminate because the prime factors of 480 include 2 and 5. Which is the correct evaluation of the student's statement?HardLevel 1What is the simplified form of ( (5\sqrt{3}-2\sqrt{5})^2 )?HardLevel 1Which of the following numbers is definitely irrational?HardLevel 1What is the rationalised form of ( \frac{1}{3\sqrt{2}+2\sqrt{5}} )?HardLevel 1What is the rationalised form of ( \frac{2}{\sqrt{7}-\sqrt{5}} )?HardLevel 1What is the value of (3 + √2)/(3 − √2) + (3 − √2)/(3 + √2)?HardLevel 5What is the value of \(\left(\sqrt{5}+\sqrt{3}\right)^2-\left(\sqrt{5}-\sqrt{3}\right)^2\)?HardLevel 1What is the value of ( \frac{\sqrt{12}+\sqrt{27}}{\sqrt{3}} )?HardLevel 1If \(x\) is an irrational number, which of the following statements is always true?HardLevel 1A student says that if the given denominator of a fraction has a prime factor other than 2 and 5, then its decimal expansion must be non-terminating. Which of the following fractions shows the error in this statement?HardLevel 1Which of the following numbers is irrational because its decimal expansion is non-terminating and non-repeating?HardLevel 1Which is the correct ascending order?HardLevel 1