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Question 6
Which among $$2^{1/2}, 3^{1/3}, 4^{1/4}, 6^{1/6}$$, and $$12^{1/12}$$ is the largest?
Solution
Make the power equal and compare the denominators.
$$2^{1/2}$$ can be written as $$64^{1/12}$$
$$3^{1/3}$$ can be written as $$81^{1/12}$$
$$4^{1/4}$$ can be written as $$64^{1/12}$$
$$6^{1/6}$$ can be written as $$36^{1/12}$$
Among these, $$81^{1/12}$$ is the greatest => $$3^{1/3}$$ is the greatest.
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