Câu 68:

Tính

a) \(\sqrt[3]{27}-\sqrt[3]{-8}-\sqrt[3]{125}\)

b) \(\frac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54} \cdot \sqrt[3]{4}\)

Lời giải:

a) \(\sqrt[3]{27}-\sqrt[3]{-8}-\sqrt[3]{125}=\sqrt[3]{3^{3}}-\sqrt[3]{(-2)^{3}}-\sqrt[3]{5^{3}}\)

\(=3-(-2)-5\)

\(=3+2-5=0\)

b) \(\frac{\sqrt[3]{135}}{\sqrt[3]{5}}-\sqrt[3]{54} \cdot \sqrt[3]{4}=\frac{\sqrt[3]{27.5}}{\sqrt[3]{5}}-\sqrt[3]{54.4}\)

\(=\frac{\sqrt[3]{5} \cdot \sqrt[3]{27}}{\sqrt[3]{5}}-\sqrt[3]{216}\)

\(=\sqrt[3]{27}-\sqrt[3]{216}\)

\(=\sqrt[3]{3^{3}}-\sqrt[3]{6^{3}}\)

\(=3-6=-3\)