1. Вычисли: а) \(\sqrt{20^2 - 16^2}\) б) \(\sqrt{40 \cdot 490}\) в) \(\sqrt{11^2 + 60^2}\) г) \(\frac{\sqrt{32}}{\sqrt{128}}\)

Решение:

1. \(\sqrt{20^2 - 16^2} = \sqrt{400 - 256} = \sqrt{144} = 12\)
2. \(\sqrt{40 \cdot 490} = \sqrt{40 \cdot 10 \cdot 49} = \sqrt{400 \cdot 49} = \sqrt{400} \cdot \sqrt{49} = 20 \cdot 7 = 140\)
3. \(\sqrt{11^2 + 60^2} = \sqrt{121 + 3600} = \sqrt{3721} = 61\)
4. \(\frac{\sqrt{32}}{\sqrt{128}} = \sqrt{\frac{32}{128}} = \sqrt{\frac{1}{4}} = \frac{1}{2}\)

Ответ: а) 12; б) 140; в) 61; г) 1/2.