839 Вправа 839Алгебра 8 клас Бевз 2025 · § 16 · стор. 157

839. Спрости вираз: а) √(12 + 2√11); б) √(6 − 4√2); в) √(67 + 12√7).

а) ${\displaystyle \sqrt{12+2\sqrt{11}}=}$${\displaystyle \sqrt{11+2\sqrt{11}+1}}$=

=${\displaystyle \sqrt{{(\sqrt{11}+1)}^2}=}$${\displaystyle \sqrt{11}+1}$;

б) ${\displaystyle \sqrt{6-4\sqrt{2}}=}$${\displaystyle \sqrt{4-2\cdot 2\sqrt{2}+2}=}$${\displaystyle \sqrt{{(2-\sqrt{2})}^2}}$=

=${\displaystyle |2-\sqrt{2}|=}$${\displaystyle 2-\sqrt{2}}$;

в) ${\displaystyle \sqrt{67+12\sqrt{7}}=}$${\displaystyle \sqrt{4+2\cdot 2\cdot 3\sqrt{7}+63}}$=

=${\displaystyle \sqrt{{(2+3\sqrt{7})}^2}=}$${\displaystyle 2+3\sqrt{7}}$.