4. Упростите выражение: 1) 7√2-3√8+4√18; 2) (√90-√40)⋅√10; 3) (3√5-2)²; 4) (2√3+3√5)(2√3-3√5).

1) 7√2 - 3√8 + 4√18 = 7√2 - 3√(4 ⋅ 2) + 4√(9 ⋅ 2) = 7√2 - 3 ⋅ 2√2 + 4 ⋅ 3√2 = 7√2 - 6√2 + 12√2 = 13√2

2) (√90 - √40) ⋅ √10 = (√(9 ⋅ 10) - √(4 ⋅ 10)) ⋅ √10 = (3√10 - 2√10) ⋅ √10 = √10 ⋅ √10 = 10

3) (3√5 - 2)² = (3√5)² - 2 ⋅ 3√5 ⋅ 2 + 2² = 9 ⋅ 5 - 12√5 + 4 = 45 - 12√5 + 4 = 49 - 12√5

4) (2√3 + 3√5)(2√3 - 3√5) = (2√3)² - (3√5)² = 4 ⋅ 3 - 9 ⋅ 5 = 12 - 45 = -33

Ответ: 1) 13√2; 2) 10; 3) 49 - 12√5; 4) -33