ГДЗ по Математике 5 Класс Номер 273 Дорофеев, Шарыгин, Суворова — Подробные Ответы

Проверьте равенство:
а) 41² + 43² + 45² = 5555;
б) 11³ + 12³ + 13³ + 14³ = 8000;
в) 2³ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + 2⁹ = 1000.

а) 41² + 43² + 45² = 1681 + 1849 + 2025 = 5555, равенство верно
б) 11³ + 12³ + 13³ + 14³ = 1331 + 1728 + 2197 + 2744 = 8000, равенство верно
в) 2³ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + 2⁹ = 8 + 32 + 64 + 128 + 256 + 512 = 1000, равенство верно

а) 41² + 43² + 45² = 5555

1. Вычисляем 41²: 41 ⋅ 41 = 1681.
2. Вычисляем 43²: 43 ⋅ 43 = 1849.
3. Вычисляем 45²: 45 ⋅ 45 = 2025.
4. Складываем: 1681 + 1849 + 2025 = 5555.
   Равенство верно.

б) 11³ + 12³ + 13³ + 14³ = 8000

1. Вычисляем 11³: 11 ⋅ 11 ⋅ 11 = 1331.
2. Вычисляем 12³: 12 ⋅ 12 ⋅ 12 = 1728.
3. Вычисляем 13³: 13 ⋅ 13 ⋅ 13 = 2197.
4. Вычисляем 14³: 14 ⋅ 14 ⋅ 14 = 2744.
5. Складываем: 1331 + 1728 + 2197 + 2744 = 8000.
   Равенство верно.

в) 2³ + 2⁵ + 2⁶ + 2⁷ + 2⁸ + 2⁹ = 1000

1. Вычисляем 2³: 2 ⋅ 2 ⋅ 2 = 8.
2. Вычисляем 2⁵: 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 32.
3. Вычисляем 2⁶: 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 64.
4. Вычисляем 2⁷: 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 128.
5. Вычисляем 2⁸: 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 256.
6. Вычисляем 2⁹: 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 ⋅ 2 = 512.
7. Складываем: 8 + 32 + 64 + 128 + 256 + 512 = 1000.
   Равенство верно.