ОГЭ 2022 (1) Вычислите: √64 . (2) Вычислите: √54.90.60 (3) Упростите: 2+√3+2-√3 (4) Вычислите: √3.7²⋅√3.24

Ответ: 1) 8; 2) 90; 3) 4; 4) 42

1. Шаг 1: Вычислим √64.

   √64 = 8

2. Шаг 2: Вычислим √54 ⋅ 90 ⋅ 60.

   √54 ⋅ 90 ⋅ 60 = √(9 ⋅ 6 ⋅ 9 ⋅ 10 ⋅ 6 ⋅ 10) = √(9² ⋅ 6² ⋅ 10²) = 9 ⋅ 6 ⋅ 10 = 540

3. Шаг 3: Упростим выражение \(\frac{1}{2 + \sqrt{3}} + \frac{1}{2 - \sqrt{3}}\).

   Для этого приведем дроби к общему знаменателю:

   \(\frac{1}{2 + \sqrt{3}} + \frac{1}{2 - \sqrt{3}} = \frac{2 - \sqrt{3} + 2 + \sqrt{3}}{(2 + \sqrt{3})(2 - \sqrt{3})} = \frac{4}{4 - 3} = \frac{4}{1} = 4\)

4. Шаг 4: Вычислим √3 ⋅ 7² ⋅ √3 ⋅ 2⁴.

   √3 ⋅ 7² ⋅ √3 ⋅ 2⁴ = √3 ⋅ √3 ⋅ 7² ⋅ 2⁴ = 3 ⋅ 49 ⋅ 16 = 3 ⋅ 7 ⋅ 7 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 42

Ответ: 1) 8; 2) 90; 3) 4; 4) 42