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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 \(\left(\sqrt{7}+\sqrt{2}\right)^2-\left(\sqrt{7}-\sqrt{2}\right)^2\)?HardLevel 2What is the value of ( \frac{\sqrt{20}+\sqrt{45}}{\sqrt{5}} )?HardLevel 2A student claims that the sum of any two irrational numbers is always irrational. Which of the following pairs is a counterexample to this claim?HardLevel 2What is the positive simplified form of ( \sqrt{14-4\sqrt{10}} )?HardLevel 2Which of the following numbers has a non-terminating, non-recurring decimal expansion?HardLevel 2If \(p/q\) is a rational number, where \(p\) and \(q\) are coprime integers and \(q>0\), which statement about its decimal expansion is correct?HardLevel 2Which is greater between ( -\sqrt{80} ) and ( -9 )?HardLevel 2What will be the decimal expansion of the simplified form of ( \frac{96}{384} )?HardLevel 2What will be the decimal expansion of the simplified form of ( \frac{132}{360} )?HardLevel 2How will (7.818181...) be classified as a real number?HardLevel 2What is the simplest form of \(\sqrt{7}+\sqrt{28}+\sqrt{63}+\sqrt{112}\)?HardLevel 2What is the value of \( \left(\frac{1}{\sqrt{7}-\sqrt{6}}\right)-\left(\frac{1}{\sqrt{7}+\sqrt{6}}\right) \)?HardLevel 2What is the value of \( \left(\frac{1}{5-\sqrt{21}}\right)+\left(\frac{1}{5+\sqrt{21}}\right) \)?HardLevel 2What is the value of \(\left(\sqrt{10}+\sqrt{3}\right)\left(\sqrt{10}-\sqrt{3}\right)\)?HardLevel 2What is the value of ( \sqrt{20}+\sqrt{180}-\sqrt{80}-\sqrt{45} )?HardLevel 2If \(x=4-\sqrt7\), what is \(\frac1x\)?MediumLevel 2If (a=\sqrt{5}+\sqrt{2}), what is the value of (a^2+\frac{1}{a^2})?HardLevel 2If (x=\sqrt{8}+3), what is the value of (x+\frac{1}{x-3})?HardLevel 2If \(a\) and \(b\) are real numbers, what is the value of \(\sqrt{(a-b)^2}\)?HardLevel 2If \(x=-9\), what is the value of \(\sqrt{x^2}+3x\)?HardLevel 2