Ответ:

4.8

1) (√15 + 3√5)² - 30√3 =

(√15)² + 2(√15)(3√5) + (3√5)² =

15 + 6√75 + 9 * 5 - 30√3 =

15 + 45 + 6√(25 * 3) - 30√3 =

60 + 6 * 5 * √3 - 30√3 =

60 + 30√3 - 30√3 = 60

2) (√(4 - √7) + √(√7 + 4))² =

(√(4 - √7))² + 2(√(4 - √7))(√(√7 + 4)) + (√(√7 + 4))² =

4 - √7 + 2√((4 - √7)(√7 + 4)) + √7 + 4 =

8 + 2√((4 - √7)(4 + √7)) =

8 + 2√(4² - (√7)²) =

8 + 2√(16 - 7) =

8 + 2√9 =

8 + 2 * 3 =

8 + 6 = 14

3) (√(5 - 2√6) + √(5 + 2√6))² =

(√(5 - 2√6))² + 2(√(5 + 2√6))(√(5 - 2√6)) + (√(5 + 2√6))² =

5 - 2√6 + 2(√(5² - (2√6)²)) + 5 + 2√6 =

10 + 2(√(25 - 4 * 6)) =

10 + 2(√(25 - 24)) =

10 + 2√1 =

10 + 2 * 1 =

10 + 2 = 12

4) (√(6 + √11) - √(6 - √11))² =

(√(6 + √11))² - 2(√(6 + √11))(√(6 - √11)) + (√(6 - √11))² =

6 + √11 - 2(√(6² - (√11)²)) + 6 - √11 =

12 - 2(√(36 - 11)) =

12 - 2√25 =

12 - 2 * 5 =

12 - 10 = 2

4.9

1) (2 - √a)(2 + √a) - 4 =

4 - (√a)² - 4 =

0 - a = -a

2) (3 - √2a)(3 + √2a) + 4a =

9 - (√2a)² + 4a =

9 - 2a + 4a = 9 + 2a

3) (2√3 - 3√a)(2√3 + 3√a) =

(2√3)² - (3√a)² =

4 * 3 - 3 * a = 12 - 3a

4) (2√7 - √7a)(2√7 + √7a) =

(2√7)² - (√7a)² =

4 * 7 - 7a = 28 - 7a