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 simplest form of \(\sqrt{72}\)?EasyLevel 6Which of the following is the simplest form of \(\sqrt{63}\)?EasyLevel 6What is the value of √2 × √50?EasyLevel 6What is the value of ( \sqrt{80}\div\sqrt{5} )?EasyLevel 6What is the simplest form of \(4\sqrt{2}+5\sqrt{2}\)?EasyLevel 6A student says that \(0.101001000100001\ldots\) is a rational number because its decimal expansion is infinite. What is the error in the student's statement?EasyLevel 6What is the simplified form of \(\sqrt{48}+\sqrt{27}\)?EasyLevel 6Rahul says that \(0.375\) is irrational because it has a decimal point. Which statement correctly explains Rahul’s mistake?EasyLevel 6Which of the following is the correct form of \(\frac{3}{\sqrt{2}}\) after rationalising the denominator?EasyLevel 6What is obtained by rationalising the denominator of ( \frac{5}{\sqrt{7}} )?EasyLevel 6What is obtained by rationalising the denominator of ( \frac{1}{2+\sqrt{3}} )?EasyLevel 6Which expression will be obtained in the numerator when the denominator of \(\frac{1}{3-\sqrt{5}}\) is rationalised?EasyLevel 6What is the value of (2+√5)(2−√5)?EasyLevel 6Which of the following is an irrational number?EasyLevel 6Which is greater between ( \sqrt{3} ) and ( \sqrt{12} )?EasyLevel 6Which is greater between ( -\sqrt{10} ) and ( -3 )?EasyLevel 6What is the value of \(\sqrt{1.44}\)?EasyLevel 6A student says that every integer is a rational number. Why is this statement correct?EasyLevel 6What is the value of \(\sqrt{\frac{25}{36}}\)?EasyLevel 6What is \(\sqrt{\frac{121}{144}}\) equal to?EasyLevel 6