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
Which is the simplified form of ( \sqrt{192} )?MediumLevel 1What is the simplified form of (3\sqrt{8}+2\sqrt{18})?MediumLevel 1A square garden has an area of 2 square metres. Which statement correctly gives the length of its side and identifies it as rational or irrational?MediumLevel 1What is the value of ( \sqrt{3}(2+\sqrt{3}) )?MediumLevel 1What is the expansion of \((2+\sqrt{7})^2\)?MediumLevel 1What is the simplified form of ( (5-\sqrt{6})^2 )?MediumLevel 1A student claims that \(\sqrt{2}+\sqrt{8}=\sqrt{10}\) because the numbers inside square roots can be added when adding square roots. Which is the correct evaluation of this claim?MediumLevel 1The area of a square is 18 cm². Which option correctly gives its side length and perimeter?MediumLevel 1What is the rationalised form of ( \frac{7}{2\sqrt{3}} )?MediumLevel 1What is the rationalised form of ( \frac{1}{\sqrt{6}+\sqrt{5}} )?MediumLevel 1Which of the following numbers has a decimal expansion that is neither terminating nor recurring?MediumLevel 1What is the simplified form of ( \sqrt{45}+\sqrt{80}-\sqrt{20} )?MediumLevel 1Choose the correct simplified form of ( \sqrt{45}+\sqrt{80}-\sqrt{20} ).MediumLevel 1Reema says that the decimal number 0.101001000100001... is rational because it uses only the digits 0 and 1. Which is the correct evaluation of her statement?MediumLevel 1Which of the following statements correctly describes the decimal expansion of irrational numbers?MediumLevel 1A student claims that the sum of two irrational numbers is always irrational. Which of the following examples disproves this claim?MediumLevel 1A student claims that the sum of two irrational numbers is always irrational. Which of the following examples disproves this statement?MediumLevel 1A square tile has a side length of 1 metre. What will be the length of its diagonal, and what type of number is it?MediumLevel 1A student classifies the number 0.101001000100001... as rational because it contains only the digits 0 and 1. Evaluate this claim correctly.MediumLevel 1What is the value of ( \sqrt{\frac{9}{16}}+\sqrt{\frac{25}{36}} )?MediumLevel 1