Rationalization (Meaning) MCQs Quiz | Class 9
Test your understanding of Class IX Mathematics (Code 041), Unit I: Number Systems. This quiz covers the meaning of rationalization, why it is done, and how to identify rationalizing factors. Submit your answers to view your score and download the PDF answer sheet.
Overview of Rationalization
In the Number Systems unit for Class 9 Mathematics, rationalization is a specific process used to rewrite fractions. A fraction is considered to be in its simplest or standard form only when its denominator is a rational number. If a denominator contains a square root or any irrational number (surd), we perform rationalization to remove it.
Why do we Rationalize?
- Standard Form: It helps in expressing the number in a universally accepted standard form.
- Ease of Calculation: Adding or subtracting fractions is significantly easier when denominators are integers rather than irrational numbers.
- Estimation: It is easier to estimate the value of a fraction like “root 2 divided by 2” than “1 divided by root 2”.
Key Concepts
Rationalizing Factor (RF): This is the term we multiply the numerator and denominator by to eliminate the radical from the bottom.
- For a simple term like 1 / root a, the RF is root a.
- For a binomial term like 1 / (a + root b), the RF is the conjugate (a – root b).
| Expression in Denominator | Rationalizing Factor (RF) | Resulting Denominator Type |
|---|---|---|
| root x | root x | Rational (x) |
| a + root b | a – root b | Rational (difference of squares) |
| root x + root y | root x – root y | Rational (x – y) |
Quick Revision List
- Rationalization converts an irrational denominator into a rational one.
- The product of an irrational number and its rationalizing factor is always rational.
- The conjugate of (root a + root b) is (root a – root b).
- We use the algebraic identity: (x + y)(x – y) = x^2 – y^2.
Extra Practice Questions
- Find the rationalizing factor of 1 / (2 + root 3).
- Rationalize the denominator of 5 / root 5.
- What is the conjugate of (root 7 – 2)?
- Simplify: 1 / (root 5 – 2).
- True or False: Rationalization changes the value of the number. (False, it only changes the form).
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