Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 415

а) $$\sqrt{8p}$$ − $$\sqrt{2p}$$ + $$\sqrt{18p}$$ = $$\sqrt{4 ⋅ 2p}$$ − $$\sqrt{2p}$$ + $$\sqrt{9 ⋅ 2p}$$ = 2$$\sqrt{2p}$$ − $$\sqrt{2p}$$ + 3$$\sqrt{2p}$$ = 4$$\sqrt{2p}$$
б) $$\sqrt{160c}$$ + 2$$\sqrt{40c}$$ − 3$$\sqrt{90c}$$ = $$\sqrt{16 ⋅ 10c}$$ + 2$$\sqrt{4 ⋅ 10c}$$ − 3$$\sqrt{9 ⋅ 10c}$$ = 4$$\sqrt{10c}$$ + 2⋅ 2$$\sqrt{10c}$$ − 3 ⋅ 3$$\sqrt{10c}$$ = 4$$\sqrt{10c}$$ + 4$$\sqrt{10c}$$ − 9$$\sqrt{10c}$$ = −$$\sqrt{10c}$$
в) 5$$\sqrt{27m}$$ − 4$$\sqrt{48m}$$ − 2$$\sqrt{12m}$$ = 5$$\sqrt{9 ⋅ 3m}$$ − 4$$\sqrt{16 ⋅ 3m}$$ − 2$$\sqrt{4 ⋅ 3m}$$ = 5 ⋅ 3$$\sqrt{3m}$$ − 4 ⋅ 4$$\sqrt{3m}$$ − 2 ⋅ 2$$\sqrt{3m}$$ = 15$$\sqrt{3m}$$ − 16$$\sqrt{3m}$$ − 4$$\sqrt{3m}$$ = −5$$\sqrt{3m}$$
г) $$\sqrt{54}$$ − $$\sqrt{24}$$ + $$\sqrt{150}$$ = $$\sqrt{9 ⋅ 6}$$ − $$\sqrt{4 ⋅ 6}$$ + $$\sqrt{25 ⋅ 6}$$ = 3$$\sqrt{6}$$ − 2$$\sqrt{6}$$ + 5$$\sqrt{6}$$ = 6$$\sqrt{6}$$
д) 3$$\sqrt{2}$$ + $$\sqrt{32}$$ − $$\sqrt{200}$$ = 3$$\sqrt{2}$$ + $$\sqrt{16 ⋅ 2}$$ − $$\sqrt{100 ⋅ 2}$$ = 3$$\sqrt{2}$$ + 4$$\sqrt{2}$$ − 10$$\sqrt{2}$$ = −3$$\sqrt{2}$$
е) 2$$\sqrt{72}$$ − $$\sqrt{50}$$ − 2$$\sqrt{8}$$ = 2$$\sqrt{36 ⋅ 2}$$ − $$\sqrt{25 ⋅ 2}$$ − 2$$\sqrt{4 ⋅ 2}$$ = 2 ⋅ 6$$\sqrt{2}$$ − 5$$\sqrt{2}$$ − 2 ⋅ 2$$\sqrt{2}$$ = 12$$\sqrt{2}$$ − 5$$\sqrt{2}$$ − 4$$\sqrt{2}$$ = 3$$\sqrt{2}$$