Tính và so sánh :
a) \(\sqrt[3]{{27}}\) với \(\sqrt[3]{{64}}\);
b) \(\sqrt[3]{{8.27}}\) với \(\sqrt[3]{8}.\sqrt[3]{{27}}\);
c) \(\sqrt[3]{{\dfrac{{64}}{{125}}}}\) với \(\dfrac{{\sqrt[3]{{64}}}}{{\sqrt[3]{{125}}}}\).
a) Ta có: \(27 < 64 \Rightarrow \sqrt[3]{{27}} < \sqrt[3]{{64}}.\)
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b) Ta có: \(\sqrt[3]{{8.27}} = \sqrt[3]{{{2^3}{{.3}^3}}} = \sqrt[3]{{{{\left( 6 \right)}^3}}} = 6.\)
\(\sqrt[3]{8}.\sqrt[3]{{27}} = \sqrt[3]{{{2^3}}}.\sqrt[3]{{{3^3}}} = 2.3 = 6.\)
Vậy \(\sqrt[3]{{8.27}} = \sqrt[3]{8}.\sqrt[3]{{27}}.\)
c) Ta có: \(\sqrt[3]{{\dfrac{{64}}{{125}}}} = \sqrt[3]{{\dfrac{{{4^3}}}{{{5^3}}}}} = \sqrt[3]{{{{\left( {\dfrac{4}{5}} \right)}^3}}} = \dfrac{4}{5}.\)
\(\dfrac{{\sqrt[3]{{64}}}}{{\sqrt[3]{{125}}}} = \dfrac{{\sqrt[3]{{{4^3}}}}}{{\sqrt[3]{{{5^3}}}}} = \dfrac{4}{5}.\)
Vậy \(\dfrac{{\sqrt[3]{{64}}}}{{\sqrt[3]{{125}}}} = \dfrac{{\sqrt[3]{{64}}}}{{\sqrt[3]{{125}}}}.\)