Основано на упр. 9 стр. 17. Сравни числа \left(\dfrac{3}{5}\right)^3 и \left(\dfrac{4}{5}\right)^3. Так как \dfrac{3}{5} \dfrac{4}{5}, то \Big(\dfrac{3}{5}\Big)^3 \Big(\dfrac{4}{5}\Big)^3. (7,01)^4 и (7,011)^4. Так как 7,01 (7,01)^4 (7,011)^4. \left(\dfrac{7}{9}\right)^{\frac{1}{2}} и \left(\dfrac{6}{7}\right)^{\frac{1}{2}}. Так как \dfrac{7}{9}= , \dfrac{6}{7}= , то \left(\dfrac{7}{9}\right)^{\frac{1}{2}} \left(\dfrac{6}{7}\right)^{\frac{1}{2}}. \sqrt[3]{0,21} и \sqrt[3]{0,31}. Так как \sqrt[3]{0,21}=(0,21),\ \sqrt[3]{0,31}=(0,31) и 0,21 0,31, то \sqrt[3]{0,21} \sqrt[3]{0,31}.

Задание

Основано на упр. 9 стр. 17.

Сравни числа

\(\left(\dfrac{3}{5}\right)^3\) и \(\left(\dfrac{4}{5}\right)^3\) . Так как \(\dfrac{3}{5}\) [ \(\gt\) | \(\lt\) | \(=\) ] \(\dfrac{4}{5}\) , то \(\Big(\dfrac{3}{5}\Big)^3\) [ \(\gt\) | \(\lt\) | \(=\) ] \(\Big(\dfrac{4}{5}\Big)^3\) .
\((7,01)^4\) и \((7,011)^4\) . Так как \(7,01\) [ \(\gt\) | \(\lt\) | \(=\) ] \((7,01)^4\) [ \(\gt\) | \(\lt\) | \(=\) ] \((7,011)^4\) .
\(\left(\dfrac{7}{9}\right)^{\frac{1}{2}}\) и \(\left(\dfrac{6}{7}\right)^{\frac{1}{2}}\) . Так как \(\dfrac{7}{9}=\) [ ], \(\dfrac{6}{7}=\) [ ], то \(\left(\dfrac{7}{9}\right)^{\frac{1}{2}}\) [ \(\gt\) | \(\lt\) | \(=\) ] \(\left(\dfrac{6}{7}\right)^{\frac{1}{2}}\) .
\(\sqrt[3]{0,21}\) и \(\sqrt[3]{0,31}\) . Так как \(\sqrt[3]{0,21}=(0,21),\ \sqrt[3]{0,31}=(0,31)\) и \(0,21\) [ \(\gt\) | \(\lt\) | \(=\) ] \(0,31\) , то \(\sqrt[3]{0,21}\) [ \(\gt\) | \(\lt\) | \(=\) ] \(\sqrt[3]{0,31}\) .