560 Вправа 560Алгебра 8 клас Тарасенкова 2025 · § 13 · стор. 162

560. Спростіть вираз:

1) ${\displaystyle \sqrt{0,9}(\sqrt{0,1}+\sqrt{0,4})=}$${\displaystyle \sqrt{0,9}\cdot \sqrt{0,1}+\sqrt{0,9}\cdot \sqrt{0,4}=}$${\displaystyle \sqrt{0,09}+\sqrt{0,36}=}$${\displaystyle 0,3+0,6=}$${\displaystyle 0,9}$;

2) ${\displaystyle \sqrt{\frac{1}{5}}(\sqrt{20}+\sqrt{0,8})=}$${\displaystyle \sqrt{\frac{1}{5}\cdot 20}+\sqrt{\frac{1}{5}\cdot 0,8}=}$${\displaystyle \sqrt{4}+\sqrt{0,16}=}$${\displaystyle 2+0,4=}$${\displaystyle 2,4}$;

3) ${\displaystyle \sqrt{{26}^2-{10}^2}=}$${\displaystyle \sqrt{(26-10)(26+10)}=}$${\displaystyle \sqrt{16\cdot 36}=}$${\displaystyle \sqrt{16}\cdot \sqrt{36}=}$${\displaystyle 4\cdot 6=}$${\displaystyle 24}$;

4) ${\displaystyle {(2+\sqrt{11})}^2+{(2-\sqrt{11})}^2=}$${\displaystyle (4+4\sqrt{11}+11)+(4-4\sqrt{11}+11)=}$${\displaystyle 4+4\sqrt{11}+11+4-4\sqrt{11}+11=}$${\displaystyle 30}$.