Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 414

а) $$\sqrt{75}$$ + $$\sqrt{48}$$ − $$\sqrt{300}$$ = $$\sqrt{25 ⋅ 3}$$ + $$\sqrt{16 ⋅ 3}$$ − $$\sqrt{100 ⋅ 3}$$ = 5$$\sqrt{3}$$ + 4$$\sqrt{3}$$ − 10$$\sqrt{3}$$ = −$$\sqrt{3}$$
б) 3$$\sqrt{8}$$ − $$\sqrt{50}$$ + 2$$\sqrt{18}$$ = 3$$\sqrt{4 ⋅ 2}$$ − $$\sqrt{25 ⋅ 2}$$ + 2$$\sqrt{9 ⋅ 2}$$ = 3 ⋅ 2$$\sqrt{2}$$ − 5$$\sqrt{2}$$ + 2 ⋅ 3$$\sqrt{2}$$ = 6$$\sqrt{2}$$ − 5$$\sqrt{2}$$ + 6$$\sqrt{2}$$ = 7$$\sqrt{2}$$
в) $$\sqrt{242}$$ − $$\sqrt{200}$$ + $$\sqrt{8}$$ = $$\sqrt{121 ⋅ 2}$$ − $$\sqrt{100 ⋅ 2}$$ + $$\sqrt{4 ⋅ 2}$$ = 11$$\sqrt{2}$$ − 10$$\sqrt{2}$$ + 2$$\sqrt{2}$$ = 3$$\sqrt{2}$$
г) $$\sqrt{75}$$ − 0,1$$\sqrt{300}$$ − $$\sqrt{27}$$ = $$\sqrt{25 ⋅ 3}$$ − 0,1$$\sqrt{100 ⋅ 3}$$ − $$\sqrt{9 ⋅ 3}$$ = 5$$\sqrt{3}$$ − 0,1 ⋅ 10$$\sqrt{3}$$ − 3$$\sqrt{3}$$ = $$\sqrt{3}$$
д) $$\sqrt{98}$$ − $$\sqrt{72}$$ + 0,5$$\sqrt{8}$$ = $$\sqrt{49 ⋅ 2}$$ − $$\sqrt{36 ⋅ 2}$$ + 0,5$$\sqrt{4 ⋅ 2}$$ = 7$$\sqrt{2}$$ − 6$$\sqrt{2}$$ + 0,5 ⋅ 2$$\sqrt{2}$$ = 7$$\sqrt{2}$$ − 6$$\sqrt{2}$$ + $$\sqrt{2}$$ = 2$$\sqrt{2}$$