Irrational Numbers (Examples) MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) quiz focuses on Unit I: Number Systems, specifically exploring Irrational Numbers. Topics include examples like square root 2 and square root 3, their decimal expansions, and locating them on the number line. Complete the 10 MCQs below, view your score instantly, and click ‘Download Answer PDF’ to save your results for revision.
Understanding Irrational Numbers
In the Number System (Unit I), an irrational number is a number that cannot be expressed in the form p/q, where p and q are integers and q is not zero. Unlike rational numbers, irrational numbers have decimal expansions that are non-terminating and non-recurring.
Key Concepts & Examples
- Definition: Real numbers that are not rational are irrational.
- Examples: Roots of non-perfect squares such as sqrt(2), sqrt(3), sqrt(5), etc.
- The Constant Pi: Pi is a famous irrational number. While we often use 22/7 or 3.14 for calculations, these are just approximations.
- Decimal Expansion: For irrational numbers, the digits after the decimal point go on forever without a repeating pattern (e.g., 0.1010010001…).
Locating on the Number Line
Irrational numbers like sqrt(2) and sqrt(3) can be located on the number line using geometric construction based on the Pythagoras theorem.
| Number | Triangle Base | Triangle Height | Hypotenuse |
|---|---|---|---|
| sqrt(2) | 1 unit | 1 unit | sqrt(1^2 + 1^2) = sqrt(2) |
| sqrt(3) | sqrt(2) unit | 1 unit | sqrt(2 + 1) = sqrt(3) |
Operations with Irrational Numbers
- Sum/Difference: The sum or difference of a rational number and an irrational number is irrational (e.g., 2 + sqrt(3)).
- Product/Quotient: The product or quotient of a non-zero rational number with an irrational number is irrational.
- Irrationals with Irrationals: Adding, subtracting, multiplying, or dividing two irrationals may result in either a rational or an irrational number (e.g., sqrt(2) * sqrt(2) = 2, which is rational).
Practice Questions
- Visualize 3.765 on the number line using successive magnification.
- Show how sqrt(5) can be represented on the number line.
- Classify the number (2 – sqrt(5)) as rational or irrational.
- Find an irrational number between 1/7 and 2/7.
- Rationalize the denominator of 1 / (sqrt(7) – sqrt(6)).
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