9th Class Math Ex: 1.2 Question no 3, 4 | Full Explanation (New Syllabus 2025) #smartscholars #9th

n the 2025 Punjab Board's 9th-grade Mathematics curriculum, Chapter 1 delves into "Real Numbers," with Exercise 1.2 focusing on the simplification and rationalization of expressions involving radicals. Questions 3 and 4 in this exercise are pivotal for mastering these concepts.

Question 3: Simplification of Radical Expressions

This question presents students with complex radical expressions, challenging them to simplify these expressions by applying properties of square roots and rationalization techniques. The goal is to express the given radicals in their simplest form, eliminating any irrational components from the denominators.

Detailed Solution:

Identify the Radical Components: Break down the given expression into its constituent radical parts.

Simplify Individual Radicals: Simplify each radical separately by factoring out perfect squares.

Rationalize the Denominator: If a radical exists in the denominator, multiply the numerator and the denominator by the conjugate of the denominator to eliminate the radical.

Combine and Simplify: After rationalization, combine like terms and simplify the expression to its most reduced form.
Question 4: Rationalizing Denominators

This question requires students to rationalize denominators containing binomial surds. The objective is to transform the expression into an equivalent form without radicals in the denominator, facilitating easier computation and a standardized form.

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