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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

If (a=\sqrt{2}) and (b=\sqrt{8}) then what is (a+b)?HardLevel 3What is the value of (\sqrt{45}-\sqrt{5})?HardLevel 3Which statement is false?HardLevel 3What is the value of (\frac{\sqrt{32}}{\sqrt{2}})?HardLevel 3A student claims that the number \(0.101001000100001\ldots\) is rational because its decimal expansion contains only 0 and 1. What is the correct evaluation of this claim?HardLevel 3What is the value of (\sqrt{7}+\sqrt{7})?HardLevel 3Which is the smallest set containing (-4)?HardLevel 3What is the value of (\sqrt{48}-2\sqrt{3})?HardLevel 3What is the value of (\sqrt{81}+\sqrt{1})?HardLevel 3What is the simplified form of (\sqrt{20}+\sqrt{5})?HardLevel 3What is the value of \(\sqrt{50}-\sqrt{8}\)?HardLevel 3A student says, “Every number with a non-terminating decimal expansion is irrational.” Which of the following examples disproves the student's statement?HardLevel 3If (x=\sqrt{6}) then what is (x\times x)?HardLevel 3A student claims that every non-terminating decimal is irrational. Which of the following numbers proves the student's claim wrong?HardLevel 3If (a=\sqrt{3}) then what is (2a+\sqrt{3})?HardLevel 3Which statement is not correct?HardLevel 3What is the simplified form of (\sqrt{24}+\sqrt{54})?HardLevel 3Which number is not an integer?HardLevel 3Riya writes the number \(0.101001000100001\ldots\), in which the number of zeros between successive 1s keeps increasing. She says that since the number contains only 0 and 1, it is rational. What is the correct evaluation of Riya’s statement?HardLevel 3What is the simplified form of (\sqrt{72})?HardLevel 3