Алгебра 8 класс учебник Макарычев, Миндюк ответы – номер 408

а) 1/3$$\sqrt{351}$$ = $$ =\sqrt{\left(\frac{1}{3}\right)^2 \square 351}=\sqrt{\frac{1}{9} B 51}=\sqrt{\frac{1351 \div 9}{9 \div 9}} $$ = $$\sqrt{39}$$ 1/2$$\sqrt{188}$$ = $$ \sqrt{\left(\frac{1}{2}\right)^2 \square 88}=\sqrt{\frac{1}{4} \square 88}=\sqrt{\frac{1188 \div 4}{4 \div 4}}= $$ = $$\sqrt{47}$$ $$\sqrt{39}$$ < $$\sqrt{47}$$ 1/3$$\sqrt{351}$$ < 1/2$$\sqrt{188}$$
б) 1/3$$\sqrt{54}$$ = $$ \sqrt{\left(\frac{1}{3}\right)^2 54}=\sqrt{\frac{1}{9} 54}=\sqrt{\frac{154 \div 9}{9 \div 9}} $$ = $$\sqrt{6}$$ 1/5$$\sqrt{150}$$ = $$ \sqrt{\left(\frac{1}{5}\right)^2 \square 50}=\sqrt{\frac{1}{25} \square 50}=\sqrt{\frac{1150 \div 25}{25 \div 25}} $$ = $$\sqrt{6}$$ $$\sqrt{6}$$ = $$\sqrt{6}$$ 1/3$$\sqrt{54}$$ = 1/5$$\sqrt{150}$$
в) 1/3$$\sqrt{216}$$ = $$ \sqrt{\left(\frac{1}{3}\right)^2 \square 216}=\sqrt{\frac{1}{9} \square 216}=\sqrt{\frac{1216 \div 9}{9 \div 9}} $$ = $$\sqrt{24}$$ $$\sqrt{24}$$ = $$\sqrt{24}$$ $$\sqrt{24}$$ = 1/3$$\sqrt{216}$$
г) 2/3$$\sqrt{72}$$ = $$ \sqrt{\left(\frac{2}{3}\right)^2 \square 72}=\sqrt{\frac{4}{9} \square 72}=\sqrt{\frac{4 \square 72 \div 9}{9 \div 9}} $$ = $$\sqrt{4 ⋅ 8}$$ = $$\sqrt{32}$$ $$ 7 \sqrt{\frac{2}{3}}=\sqrt{7^2 \frac{2}{3}}=\sqrt{49 \frac{2}{3}}=\sqrt{\frac{49 \sqsubset 2}{3}}=\sqrt{\frac{98}{3}}=\sqrt{32 \frac{2}{3}} $$ $$\sqrt{32}$$ < $$ \sqrt{32 \frac{2}{3}} $$ 2/3$$\sqrt{72}$$ < 7$$ \sqrt{\frac{2}{3}} . $$