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The value of $${\text{ }}\root 3 \of {\frac{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}{{0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08}}} $$        is ?

The value of $${\text{ }}\root 3 \of {\frac{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}{{0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08}}} $$        is ? Correct Answer 0.5

$$\eqalign{ & = \root 3 \of {\frac{{0.2 \times 0.2 \times 0.2 + 0.04 \times 0.04 \times 0.04}}{{0.4 \times 0.4 \times 0.4 + 0.08 \times 0.08 \times 0.08}}} \cr & = \root 3 \of {\frac{{0.008 + 0.000064}}{{0.064 + 0.000512}}} \cr & = \root 3 \of {\frac{{0.008064}}{{0.064512}}} \cr & = \root 3 \of {\frac{{8064}}{{64512}}} \cr & = \root 3 \of {\frac{1}{8}} \cr & = \frac{1}{2} \cr & = 0.5 \cr} $$

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