Question 26

The value of $$(5\sqrt[3]{4}-3\sqrt[3]{\frac{1}{2}})(12\sqrt[3]{2}+\sqrt[3]{16}-2\sqrt[3]{2})$$ is

Correct Answer: 84

Solution

Let $$t=\sqrt[3]{2}$$, so $$t^3=2$$, $$\sqrt[3]{4}=t^2$$, $$\sqrt[3]{\frac{1}{2}}=\frac{1}{t}$$ and $$\sqrt[3]{16}=2t$$. The expression becomes $$\left(5t^2-\frac{3}{t}\right)(12t)$$. This equals $$12(5t^3-3)=12(10-3)=84$$.

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