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

  1. Identify the denominator’s conjugate by changing the sign between the terms.
  2. Multiply numerator and denominator by this conjugate.
  3. Simplify the denominator using A^2 – B^2.
  4. 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)