Class 9 Math Exercise 1.5 | Question 2

Question 2: Simplify each of the following expressions:
(i) (3 + √3) (2 + √2)
(ii) (3 + √3) (3 - √3)
(iii) (√5 + √2)²
(iv) (√5 - √2)(√5 + √2)

Explanatory Answer | Exercise 1.5 Question 2

Simplify: (i) (3 + √3) (2 + √2)

Expand the terms in the parantheses by Binomial Multiplication
6 + 2√3 + 3√2 + √6

Simplify: (ii) (3 + √3) (3 - √3)

The given expression is of the form (a + b)(a – b)
(a + b)(a – b) = a² - b²
∴ (3 + √3) (3 - √3) = 3² - (√3)²
= 9 - 3 = 6

Simplify: (iii) (√5 + √2)²

The given expression is of the form (a + b)²
(a + b)² = a² + b² + 2ab
∴ (√5 + √2)² = (√5)² + (√2)² + 2√5√2
= 5 + 2 + 2√10 = 7 + 2√10

Simplify: (iv) (√5 - √2)(√5 + √2)

The given expression is of the form (a + b)(a – b)
(a + b)(a – b) = a² - b²
∴ (√5 - √2 )( √5 + √2 ) = (√5)² - (√2)²
= 5 - 2 = 3