Выполни примеры с доски: 1) √484-169=

Привет! Давай по порядку решим примеры с доски. 1) $\sqrt{484} - \sqrt{169} = 22 - 13 = 9$ 2) $\sqrt{4,41} \cdot \sqrt{121} = 2,1 \cdot 11 = 23,1$ 3) $\sqrt{\frac{1}{81}} = \frac{1}{9}$ 4) $\sqrt{\frac{25}{81} \cdot \frac{16}{49} \cdot \frac{196}{9}} = \frac{5}{9} \cdot \frac{4}{7} \cdot \frac{14}{3} = \frac{5 \cdot 4 \cdot 14}{9 \cdot 7 \cdot 3} = \frac{280}{189} = \frac{40}{27} \approx 1,48$ 5) $\sqrt{2} \cdot \sqrt{8} = \sqrt{2 \cdot 8} = \sqrt{16} = 4$ 6) $\frac{\sqrt{23}}{\sqrt{2300}} = \sqrt{\frac{23}{2300}} = \sqrt{\frac{1}{100}} = \frac{1}{10} = 0,1$ 7) $\frac{\sqrt{999}}{\sqrt{111}} = \sqrt{\frac{999}{111}} = \sqrt{9} = 3$ 8) $\sqrt[3]{125} = 5$ 9) $\sqrt[3]{7^{12}} = 7^{\frac{12}{3}} = 7^4 = 2401$ 10) $\sqrt[3]{108} = \sqrt[3]{27 \cdot 4} = 3\sqrt[3]{4}$ 11) $\frac{x}{\sqrt{5}} = \frac{x \cdot \sqrt{5}}{5}$ 12) $\frac{6}{2\sqrt{3}} = \frac{3}{\sqrt{3}} = \frac{3\sqrt{3}}{3} = \sqrt{3}$ 13) $\frac{a}{\sqrt{a+b}} = \frac{a\sqrt{a+b}}{a+b}$ 14) $\frac{a}{\sqrt{a} - \sqrt{b}} = \frac{a(\sqrt{a} + \sqrt{b})}{a-b}$ 15) $\sqrt{75} + \sqrt{48} - \sqrt{300} = \sqrt{25 \cdot 3} + \sqrt{16 \cdot 3} - \sqrt{100 \cdot 3} = 5\sqrt{3} + 4\sqrt{3} - 10\sqrt{3} = -\sqrt{3}$ 16) $\sqrt{8p} - \sqrt{2p} + \sqrt{16p} = 2\sqrt{2p} - \sqrt{2p} + 4\sqrt{p} = \sqrt{2p} + 4\sqrt{p}$