32 Вправа 32 (повторення)Алгебра 8 клас Тарасенкова 2025 · Повторення · стор. 320

32. Спростіть вираз:

1) ${\displaystyle 10\sqrt{5}+20\sqrt{5}-25\sqrt{5}=}$${\displaystyle (10+20-25)\sqrt{5}=}$${\displaystyle 5\sqrt{5}}$;

2) ${\displaystyle (\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})+{(\sqrt{3}+\sqrt{5})}^2=}$${\displaystyle {\left(\sqrt{5}\right)}^2-{\left(\sqrt{3}\right)}^2+{\left(\sqrt{3}\right)}^2+2\sqrt{3}\cdot \sqrt{5}+{\left(\sqrt{5}\right)}^2=}$${\displaystyle 5\cancel{-3}\cancel{+3}+2\sqrt{15}+5=}$${\displaystyle 10+2\sqrt{15}}$;

3) ${\displaystyle {\left(\sqrt{3+\sqrt{2}}\right)}^2-\sqrt{{(1-\sqrt{2})}^2}=}$${\displaystyle 3+\sqrt{2}-|1-\sqrt{2}|=}$${\displaystyle 3+\sqrt{2}-(\sqrt{2}-1)=}$${\displaystyle 3\cancel{+\sqrt{2}}\cancel{-\sqrt{2}}+1=}$${\displaystyle 4}$.