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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 correct simplified form of ( |4-\sqrt{27}| )?HardLevel 2A student says that the product of two irrational numbers is always irrational. Which of the following examples proves the statement wrong?HardLevel 2Which statement is correct about \(\sqrt{32}+\sqrt{18}\) and \(7\sqrt{2}\)?HardLevel 2If \(x\) is an irrational number and \(r\) is a rational number, which of the following statements is always true?HardLevel 2Which of the following statements about rational and irrational numbers is correct?HardLevel 2What is the value of (1/(√13+2)+1/(√13−2))?HardLevel 2What is the simplified form of ( (3+\sqrt{5})^3 )?HardLevel 2What is the simplified form of ( (4-\sqrt{3})^3 )?HardLevel 2If ( \sqrt{n} ) lies between (18) and (19), which range is correct for (n)?HardLevel 2If \(21<\sqrt{m}<22\), which range is correct for \(m\)?HardLevel 2Which example shows that \(\sqrt{a+b}=\sqrt a+\sqrt b\) is false?MediumLevel 2What is the value of ( \sqrt{ab}\times\sqrt{ab} ) where (ab\geq0)?HardLevel 2What is the correct statement about ( \sqrt{36}+\sqrt{49} ) and ( \sqrt{85} )?HardLevel 2Which product gives a rational number?HardLevel 2If (0.1010010001\ldots) is the decimal expansion then this number is?HardLevel 3What is the value of (2\sqrt{3}+\sqrt{27})?HardLevel 3A student says that if the decimal expansion of a number is non-terminating and non-repeating, then the number is irrational. What is the correct analysis of this statement?HardLevel 3If (x=\sqrt{5}) then what is (x^2)?HardLevel 3What is the simplified form of (\sqrt{12}+\sqrt{27})?HardLevel 3A student says that if the decimal expansion of a number is non-terminating, then the number must be irrational. Which example disproves this statement?HardLevel 3