6. a) √(⁵√32+∛8) = √(2+2) = √4 = 2 b) ⁶√(∛27+⁶√64-∛125) =⁶√(3+2-5) = ⁶√(5-5) = ⁶√0 = 0 c) 2⁵√(243/1024) + ⁶√(1/64) = 2·¾+½ = 2 d) ∛(-⁴√16+∛-216) = ∛(-2-6) = ∛-8 = -2 7. b) 2√175-3√98+3√18-2√112 = = 2√(25·7) - 3√(49·2) + 3√(9·2) - 2√(16·7) = = 2·5√7 - 3·7√2 + 3·3√2 - 2·4√7 = = 10√7-21√2+9√2-8√7 = = 2√7-12√2 = = 2(√7-6√2) c) ⅖√125 - ⅔√243 - ⅓√45 + ½√48 = = ⅖√(25·5) - ⅔√(81·3) - ⅓√(9·5) + ½√(16·3) = = ⅖·5√5 - ⅔·9√3 - ⅓·3√5 + ½·4√3 = = 2√5-6√3-√5+2√3 = = √5-4√3 8. a) (3√2+2√5)(3√2-2√5) = (3√2)²-(2√5)² = 18-20 = -2 b) (3√7-√2)² = (3√7)²-2·3√7·√2+(√2)² = 63-6√14+2 = 65-6√14 c) (√6+2√3)² = (√6)²+2·√6·2√3+(2√3)² = 6+4√18+12 = 18+4·3√2 = 18+12√2 d) (2∛3+3∛2)² = (2∛3)²+2·2∛3·3∛2+(3∛2)² = 4∛9+12∛6+9∛4
