Bài 9: Căn bậc ba

\(=\left(\sqrt[3]{3}\right)^3+3\cdot\sqrt[3]{3^2}\cdot\sqrt[3]{2}+3\cdot\sqrt[3]{3\cdot2^2}+2\)

\(=5+3\cdot\sqrt[3]{18}+3\sqrt[3]{12}\)

gần bằng 19,731

\(\left(\sqrt[3]{3}+\sqrt[3]{2}\right)^3=\left(\sqrt[3]{3}\right)^3+3\left(\sqrt[3]{3}\right)^2\sqrt[3]{2}+3\sqrt[3]{3}\left(\sqrt[3]{2}\right)^2+\left(\sqrt[3]{2}\right)^3\)

\(=3+3\sqrt[3]{18}+3\sqrt[3]{12}+2=5+3\sqrt[3]{18}+3\sqrt[3]{12}\)

\(E=\left(\sqrt[3]{2}+1\right)\sqrt[3]{\dfrac{\sqrt[3]{2}-1}{3}}\Rightarrow E^3=\dfrac{\sqrt[3]{2}-1}{3}.\left(2+1+3\sqrt[3]{2}+3\sqrt[3]{2}^2\right)=\dfrac{\sqrt[3]{2}-1}{3}.3\left(1+\sqrt[3]{2}+\sqrt[3]{2}^2\right)=\left(\sqrt[3]{2}-1\right)\left(\sqrt[3]{2}\left(\sqrt[3]{2}+1\right)+1\right)=\sqrt[3]{2}\left(\sqrt[3]{2}^2-1\right)+\sqrt[3]{2}-1=2-\sqrt[3]{2}+\sqrt[3]{2}-1=1\Rightarrow E=1\in Z\)

Câu 1: A

Câu 2: B

4+(-2)+5=7

\(\sqrt[3]{64}+\sqrt[3]{-8}+\sqrt[3]{125}=4+\left(-2\right)+5=7\)

=7

\(=-10+3\sqrt[3]{2}-8\sqrt[3]{2}=-10-5\sqrt[3]{2}\)