Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 409

а) 3$$\sqrt{3}$$ = $$\sqrt{3² ⋅ 3}$$ = $$\sqrt{9 ⋅ 3}$$ = $$\sqrt{27}$$
2$$\sqrt{6}$$ = $$\sqrt{2² ⋅ 6}$$ = $$\sqrt{4 ⋅ 6}$$ = $$\sqrt{24}$$
4$$\sqrt{2}$$ = $$\sqrt{4² ⋅ 2}$$ = $$\sqrt{16 ⋅ 2}$$ = $$\sqrt{32}$$
2$$\sqrt{11}$$ = $$\sqrt{2² ⋅ 11}$$ = $$\sqrt{4 ⋅ 11}$$ = $$\sqrt{44}$$
$$\sqrt{24}$$, $$\sqrt{27}$$, $$\sqrt{29}$$, $$\sqrt{32}$$, $$\sqrt{44}$$
2$$\sqrt{6}$$, 3$$\sqrt{3}$$, $$\sqrt{29}$$, 4$$\sqrt{2}$$, 2$$\sqrt{11}$$
б) 6$$\sqrt{2}$$ = $$\sqrt{6² ⋅ 2}$$ = $$\sqrt{36 ⋅ 2}$$ = $$\sqrt{72}$$
3$$\sqrt{7}$$ = $$\sqrt{3² ⋅ 7}$$ = $$\sqrt{9 ⋅ 7}$$ = $$\sqrt{63}$$
2$$\sqrt{14}$$ = $$\sqrt{2² ⋅ 14}$$ = $$\sqrt{4 ⋅ 14}$$ = $$\sqrt{56}$$
5$$\sqrt{3}$$ = $$\sqrt{5² ⋅ 3}$$ = $$\sqrt{25 ⋅ 3}$$ = $$\sqrt{75}$$
$$\sqrt{56}$$, $$\sqrt{58}$$, $$\sqrt{63}$$, $$\sqrt{70}$$, $$\sqrt{75}$$
2$$\sqrt{14}$$, $$\sqrt{58}$$, 3$$\sqrt{7}$$, 6$$\sqrt{2}$$, 5$$\sqrt{3}$$
в) −2$$\sqrt{5}$$ = −$$\sqrt{2² ⋅ 5}$$ = −$$\sqrt{4 ⋅ 5}$$ = −$$\sqrt{20}$$
−2$$\sqrt{6}$$ = −$$\sqrt{2² ⋅ 6}$$ = −$$\sqrt{4 ⋅ 6}$$ = −$$\sqrt{24}$$
−$$\sqrt{51}$$, −$$\sqrt{24}$$, −$$\sqrt{20}$$, −$$\sqrt{11}$$, $$\sqrt{2}$$
−$$\sqrt{51}$$, −2$$\sqrt{6}$$, −2$$\sqrt{5}$$, −$$\sqrt{11}$$, $$\sqrt{2}$$
г) −9$$\sqrt{2}$$ = −$$\sqrt{9² ⋅ 2}$$ = −$$\sqrt{81 ⋅ 2}$$ = −$$\sqrt{162}$$
−5$$\sqrt{8}$$ = −$$\sqrt{5² ⋅ 8}$$ = −$$\sqrt{25 ⋅ 8}$$ = −$$\sqrt{200}$$
−1/3$$\sqrt{18}$$ = $$ -\sqrt{\left(\frac{1}{3}\right)^2 \square 8}=-\sqrt{\frac{1}{9} \square 18}=-\sqrt{\frac{118 \div 9}{9 \div 9}}= $$ = $$\sqrt{2}$$
−$$\sqrt{200}$$, −$$\sqrt{162}$$, −$$\sqrt{83}$$, −$$\sqrt{17}$$, −$$\sqrt{2}$$
−5$$\sqrt{8}$$, −9$$\sqrt{2}$$, −$$\sqrt{83}$$, −$$\sqrt{17}$$, −$$\sqrt{2}$$