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Question

Evaluate: $$\sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064}$$.


Solution

As per question,
$$= \sqrt[3]{27} + \sqrt[3]{0.008} + \sqrt[3]{0.064} = (27)^{\frac{1}{3}} + (0.008)^{\frac{1}{3}} + (0.064)^{\frac{1}{3}}$$
$$= (3 \times 3 \times 3)^{\frac{1}{3}} + (0.2 \times 0.2 \times 0.2)^{\frac{1}{3}} + (0.4 \times 0.4 \times 0.4)^{\frac{1}{3}}$$
$$= (3)^{3\times \frac{1}{3}} + (0.2)^{3\times \frac{1}{3}} + (0.8)^{3\times \frac{1}{3}} = 3 + 0.2 + 0.8 = 3.6$$

Mathematics

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