Rationalization: Surds Type 1 MCQs Quiz | Class 9

This Class IX Mathematics (Code 041) quiz focuses on Unit I: Number Systems. Test your skills on Rationalization, specifically numbers of type 1/(a+root b), using conjugates and simplification. Submit your answers to view the results and download the PDF solution sheet.

Understanding Rationalization of Surds

In Class 9 Number Systems, rationalization is the process of converting an irrational denominator into a rational number. This is crucial for simplifying expressions and performing arithmetic operations on surds.

Key Concept: The Conjugate

To rationalize a denominator of the form a + root b, we multiply both the numerator and the denominator by its conjugate.

  • The conjugate of (a + root b) is (a – root b).
  • The conjugate of (a – root b) is (a + root b).

When you multiply a binomial surd by its conjugate, the result is rational because of the algebraic identity:

(x + y)(x – y) = x^2 – y^2

Steps to Simplify 1 / (a + root b)

  1. Identify the denominator (e.g., 3 + root 2).
  2. Find the conjugate by changing the sign (e.g., 3 – root 2).
  3. Multiply the numerator and denominator by this conjugate.
  4. Simplify the denominator using difference of squares.

Quick Revision List

  • Surd: An irrational root of a rational number (e.g., root 2, root 3).
  • Rationalizing Factor (RF): The term used to multiply the surd to make it rational.
  • Type 1: Simple denominators like (a + root b) or (root a + root b).

Extra Practice Questions

  1. Rationalize the denominator of 1 / (root 5 + root 2).
  2. If x = 3 + 2 root 2, find the value of (x + 1/x).
  3. Simplify: (root 3 – 1) / (root 3 + 1).
  4. Find ‘a’ and ‘b’ if (5 + 2 root 3)/(7 + 4 root 3) = a + b root 3.
  5. Evaluate 1 / (2 root 2 – root 3).