816 Вправа 816Алгебра 8 клас Бевз 2025 · § 16 · стор. 154

816. Виконай дії.

а) ${\displaystyle \sqrt{6}(\sqrt{50}+\sqrt{32})-10\sqrt{3}}$=

=${\displaystyle \sqrt{300}+\sqrt{192}-10\sqrt{3}}$=

=${\displaystyle 10\sqrt{3}+8\sqrt{3}-10\sqrt{3}=}$${\displaystyle 8\sqrt{3}}$;

б) ${\displaystyle 2\sqrt{10}(\sqrt{45}-\sqrt{80})+\sqrt{200}}$=

=${\displaystyle 2\sqrt{450}-2\sqrt{800}+\sqrt{200}}$=

=${\displaystyle 30\sqrt{2}-40\sqrt{2}+10\sqrt{2}=}$${\displaystyle 0}$;

в) ${\displaystyle (\sqrt{42}-\sqrt{189})\cdot \sqrt{21}-21\sqrt{2}}$=

=${\displaystyle \sqrt{882}-\sqrt{3969}-21\sqrt{2}}$=

=${\displaystyle 21\sqrt{2}-63-21\sqrt{2}=}$${\displaystyle -63}$;

г) ${\displaystyle (\sqrt{56}-\sqrt{63})\cdot \sqrt{14}+\sqrt{800}}$=

=${\displaystyle \sqrt{784}-\sqrt{882}+\sqrt{800}}$=

=${\displaystyle 28-21\sqrt{2}+20\sqrt{2}=}$${\displaystyle 28-\sqrt{2}}$.

(${\displaystyle \sqrt{882}=}$${\displaystyle \sqrt{441\cdot 2}=}$${\displaystyle 21\sqrt{2}}$;

${\displaystyle \sqrt{3969}=}$${\displaystyle 63}$)