819 Вправа 819Алгебра 8 клас Бевз 2025 · § 16 · стор. 155

819. Обчисли.

а) ${\displaystyle (4\sqrt{12}-6\sqrt{48}+5\sqrt{27})\cdot \sqrt{3}-12}$=

=${\displaystyle 4\sqrt{36}-6\sqrt{144}+5\sqrt{81}-12}$=

=${\displaystyle 24-72+45-12=}$${\displaystyle -15}$;

б) ${\displaystyle {(2\sqrt{320}-7\sqrt{20}-\sqrt{45})}^2+20}$=

=${\displaystyle {(16\sqrt{5}-14\sqrt{5}-3\sqrt{5})}^2+20}$=

=${\displaystyle {(-\sqrt{5})}^2+20=}$${\displaystyle 5+20=}$${\displaystyle 25}$;

в) ${\displaystyle (\sqrt{28}+\sqrt{63}):\sqrt{7}=}$${\displaystyle (2\sqrt{7}+3\sqrt{7}):\sqrt{7}}$=

=${\displaystyle 5\sqrt{7}:\sqrt{7}=}$${\displaystyle 5}$;

г) ${\displaystyle \frac{3\sqrt{28}+2\sqrt{175}}{2\sqrt{112}}=}$${\displaystyle \frac{6\sqrt{7}+10\sqrt{7}}{8\sqrt{7}}=}$${\displaystyle \frac{16\sqrt{7}}{8\sqrt{7}}=}$${\displaystyle 2}$.