Rationalization: Surds Type 2 MCQs Quiz | Class 9
This Class IX Mathematics (Code 041) Unit I: Number Systems quiz covers Rationalization: Surds Type 2. The questions focus on numbers of type 1/(sqrt(a)+sqrt(b)), algebraic combinations, and simplification techniques. Click Submit to see your score and download the answer key PDF.
Understanding Rationalization of Type 2 Surds
Rationalization is the process of eliminating a radical (surd) from the denominator of a fraction. In Type 2 problems, the denominator typically involves a binomial expression containing square roots, such as 1 / (sqrt(a) + sqrt(b)) or 1 / (a + sqrt(b)).
Key Concepts
- Conjugate: The conjugate of a binomial expression x + y is x – y. Similarly, the conjugate of sqrt(a) + sqrt(b) is sqrt(a) – sqrt(b).
- Method: To rationalize the denominator, multiply both the numerator and the denominator by the conjugate of the denominator.
- Algebraic Identity: This process relies on the difference of squares identity: (A + B)(A – B) = A^2 – B^2. This identity removes the square roots because (sqrt(x))^2 = x.
Common Forms
| Expression | Rationalizing Factor | Resulting Denominator |
|---|---|---|
| 1 / (sqrt(a) + sqrt(b)) | sqrt(a) – sqrt(b) | a – b |
| 1 / (a + sqrt(b)) | a – sqrt(b) | a^2 – b |
| 1 / (sqrt(a) – sqrt(b)) | sqrt(a) + sqrt(b) | a – b |
Quick Revision Points
- Identify the denominator’s conjugate by changing the sign between the terms.
- Multiply numerator and denominator by this conjugate.
- Simplify the denominator using A^2 – B^2.
- Simplify the numerator and reduce the fraction if possible.
Extra Practice Questions
Try solving these on paper:
- 1. Rationalize: 1 / (root 5 + root 2)
- 2. Simplify: (4 + root 5) / (4 – root 5)
- 3. Find ‘a’ and ‘b’ if (root 3 – 1)/(root 3 + 1) = a + b(root 3).
- 4. Evaluate: 1 / (3 + 2 root 2)
- 5. Simplify: 1 / (root 3 – root 2) – 1 / (root 3 + root 2)
