818 Вправа 818Алгебра 8 клас Бевз 2025 · § 16 · стор. 155

818. Обчисли.

а) ${\displaystyle (3\sqrt{32}+\sqrt{162}-2\sqrt{288})\cdot \sqrt{2}+15}$=

=${\displaystyle 3\sqrt{64}+\sqrt{324}-2\sqrt{576}+15}$=

=${\displaystyle 24+18-48+15=}$${\displaystyle 9}$;

б) ${\displaystyle {(4\sqrt{150}-6\sqrt{54}+2\sqrt{96})}^2-20}$=

=${\displaystyle {(20\sqrt{6}-18\sqrt{6}+8\sqrt{6})}^2-20}$=

=${\displaystyle {\left(10\sqrt{6}\right)}^2-20=}$${\displaystyle 600-20=}$${\displaystyle 580}$;

в) ${\displaystyle (\sqrt{45}-\sqrt{20}):\sqrt{5}=}$${\displaystyle (3\sqrt{5}-2\sqrt{5}):\sqrt{5}}$=

=${\displaystyle \sqrt{5}:\sqrt{5}=}$${\displaystyle 1}$;

г) ${\displaystyle \frac{7\sqrt{108}-\sqrt{12}}{2\sqrt{75}}=}$${\displaystyle \frac{42\sqrt{3}-2\sqrt{3}}{10\sqrt{3}}=}$${\displaystyle \frac{40\sqrt{3}}{10\sqrt{3}}=}$${\displaystyle 4}$.