Đề bài
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 \[\dfrac{{\sqrt[3]{{64}}}}{{\sqrt[3]{{125}}}}\].
Lời giải chi tiết
a] Ta có: \[27 < 64 \Rightarrow \sqrt[3]{{27}} < \sqrt[3]{{64}}.\]
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 \[\dfrac{{\sqrt[3]{{64}}}}{{\sqrt[3]{{125}}}} = \dfrac{{\sqrt[3]{{64}}}}{{\sqrt[3]{{125}}}}.\]