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Question 11
Which of the following statement(s) is/are true?
$$I. (65)^{\frac{1}{6}} > (17)^{\frac{1}{4}} > (12)^{\frac{1}{3}}$$
$$II. (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}} > (12)^{\frac{1}{3}}$$
$$III. (12)^{\frac{1}{3}} > (17)^{\frac{1}{4}} > (65)^{\frac{1}{6}}$$
Solution
$$(65)^{\frac{1}{6}} , (17)^{\frac{1}{4}} , (12)^{\frac{1}{3}}$$
$$(12)^{\frac{1}{3}}$$=$$(144)^{\frac{1}{6}}$$
So $$(144)^{\frac{1}{6}}$$>$$(65)^{\frac{1}{6}} $$
$$(65)^{\frac{1}{6}}Â $$=$$(4225)^{\frac{1}{12}}Â $$
$$(17)^{\frac{1}{4}}$$=$$(4913)^{\frac{1}{12}}Â $$
Therefore $$(12)^{\frac{1}{3}}$$ >Â $$(17)^{\frac{1}{4}}$$ >$$(65)^{\frac{1}{6}}Â $$
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