Задание 484

\(0{,}2\sqrt{200} = 0{,}2 \cdot 10\sqrt{2} = 2\sqrt{2}\), \(10\sqrt{8} = 10 \cdot 2\sqrt{2} = 20\sqrt{2}\).

Так как \(2\sqrt{2} < 20\sqrt{2}\), то \(0{,}2\sqrt{200} < 10\sqrt{8}\).

\(7\sqrt{\dfrac{32}{49}} = 7 \cdot \dfrac{\sqrt{32}}{7} = \sqrt{32} = 4\sqrt{2}\), \(0{,}8\sqrt{50} = 0{,}8 \cdot 5\sqrt{2} = 4\sqrt{2}\).

Числа равны.

\(0{,}5\sqrt{108} = 0{,}5 \cdot 6\sqrt{3} = 3\sqrt{3}\).

Так как \(3\sqrt{3} < 9\sqrt{3}\), то \(0{,}5\sqrt{108} < 9\sqrt{3}\).

\(\dfrac{5}{2}\sqrt{63} = \dfrac{5}{2} \cdot 3\sqrt{7} = 7{,}5\sqrt{7}\), \(4{,}5\sqrt{28} = 4{,}5 \cdot 2\sqrt{7} = 9\sqrt{7}\).

Так как \(7{,}5\sqrt{7} < 9\sqrt{7}\), то \(\dfrac{5}{2}\sqrt{63} < 4{,}5\sqrt{28}\).