Сравните: а) 1/2√28 и 1/3√54 б) 7√1/7 и 1/2√20

а) [latex] \frac{1}{2} \sqrt{28} \ \textgreater \ \frac{1}{3} \sqrt{54} [/latex] б) [latex]7 \sqrt{ \frac{1}{7} } \ \textgreater \ \frac{1}{2} \sqrt{20} [/latex]

а) [latex] \frac{1}{2} \sqrt{28}= \sqrt{ \frac{1}{4}*28 } = \sqrt{7} [/latex] [latex] \frac{1}{3} \sqrt{54} = \sqrt{ \frac{1}{9}*54 }= \sqrt{6} [/latex] [latex] \sqrt{7}\ \textgreater \ \sqrt{6} [/latex] , следовательно [latex] \frac{1}{2} \sqrt{28}\ \textgreater \ \frac{1}{3} \sqrt{54} [/latex] б) [latex]7 \sqrt{ \frac{1}{7} } = \sqrt{49* \frac{1}{7} } = \sqrt{7} [/latex] [latex] \frac{1}{2} \sqrt{20}= \sqrt{ \frac{1}{4} *20} = \sqrt{5} [/latex] [latex] \sqrt{7} \ \textgreater \ \sqrt{5} [/latex] , следовательно [latex]7 \sqrt{ \frac{1}{7} } \ \textgreater \ \frac{1}{2} \sqrt{20} [/latex]