Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 407

а) 3$$\sqrt{3}$$ = $$\sqrt{3² ⋅ 3}$$ = $$\sqrt{9 ⋅ 3}$$ = $$\sqrt{27}$$ $$\sqrt{27}$$ > $$\sqrt{12}$$ 3$$\sqrt{3}$$ > $$\sqrt{12}$$
б) $$\sqrt{20}$$ = $$\sqrt{3² ⋅ 5}$$ = $$\sqrt{9 ⋅ 5}$$ = $$\sqrt{45}$$ $$\sqrt{20}$$ < $$\sqrt{45}$$ $$\sqrt{20}$$ < 3$$\sqrt{5}$$
в) 5$$\sqrt{4}$$ = $$\sqrt{5² ⋅ 4}$$ = $$\sqrt{25 ⋅ 4}$$ = $$\sqrt{100}$$ 4$$\sqrt{5}$$ = $$\sqrt{4² ⋅ 5}$$ = $$\sqrt{16 ⋅ 5}$$ = $$\sqrt{80}$$ $$\sqrt{100}$$ > $$\sqrt{80}$$ 5$$\sqrt{4}$$ > 4$$\sqrt{5}$$
г) 2$$\sqrt{5}$$ = $$\sqrt{2² ⋅ 5}$$ = $$\sqrt{4 ⋅ 5}$$ = $$\sqrt{20}$$ 3$$\sqrt{2}$$ = $$\sqrt{3² ⋅ 2}$$ = $$\sqrt{9 ⋅ 2}$$ = $$\sqrt{18}$$ $$\sqrt{20}$$ > $$\sqrt{18}$$ 2$$\sqrt{5}$$ > 3$$\sqrt{2}$$
д) −3$$\sqrt{2}$$ = −$$\sqrt{3² ⋅ 2}$$ = −$$\sqrt{9 ⋅ 2}$$ = −$$\sqrt{18}$$ −$$\sqrt{14}$$ > −$$\sqrt{18}$$ −$$\sqrt{14}$$ > −3$$\sqrt{2}$$
е) −7$$\sqrt{0,17}$$ и −11$$\sqrt{0,05}$$ = −$$\sqrt{7² ⋅ 0,17}$$ = −$$\sqrt{49 ⋅ 0,17}$$ = −$$\sqrt{8,33}$$ −11$$\sqrt{0,05}$$ = −$$\sqrt{11² ⋅ 0,05}$$ = −$$\sqrt{121 ⋅ 0,05}$$ = −$$\sqrt{6,05}$$ −$$\sqrt{8,33}$$ < −$$\sqrt{6,05}$$ −7$$\sqrt{0,17}$$ < −11$$\sqrt{0,05}$$