2. Simplify each of the following expressions: (i) (3+√3)(2+√2)
Solution: (i) (3 + √3)(2 + √2) By Distributive property, (a + b) (c + d) = ac + ad + bc + bd (3 + √3)(2 + √2) = 3 × 2 + 3√2 + √3 × 2 + √3 × √2 = 6 + 3√2 + 2√3 + √6 (ii) (3 + √3)(3 - √3) Using the identity, (a + b) (a - b) = a² - b² (3 + √3)(3 - √3) = 3² - (√3)² = 9 - 3 = 6
