831 Вправа 831Алгебра 8 клас Бевз 2025 · § 16 · стор. 156

831. Спрости вираз.

а) ${\displaystyle {(\sqrt{5}+3)}^2-{(\sqrt{5}-3)}^2}$=

=${\displaystyle (14+6\sqrt{5})-(14-6\sqrt{5})=}$${\displaystyle 12\sqrt{5}}$;

б) ${\displaystyle (14+6\sqrt{5}){(3-\sqrt{5})}^2}$=

=${\displaystyle (14+6\sqrt{5})(14-6\sqrt{5})=}$${\displaystyle 196-180=}$${\displaystyle 16}$;

в) ${\displaystyle \sqrt{10+2\sqrt{21}}\cdot \sqrt{10-2\sqrt{21}}=}$${\displaystyle \sqrt{100-84}}$=

=${\displaystyle \sqrt{16}=}$${\displaystyle 4}$;

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

=${\displaystyle 6+\sqrt{20}-2\sqrt{36-20}+6-\sqrt{20}}$=

=${\displaystyle 12-2\cdot 4=}$${\displaystyle 4}$.