Question 14

If x = $$\sqrt[6]{5}$$ and y = $$\sqrt[5]{4}$$, Which of the following is true?

Solution

Given x = $$\sqrt[6]{5}$$ and y = $$\sqrt[5]{4}$$

which can also be written as x = $$5^{\frac{5}{30}}$$ and y = $$4^{\frac{6}{30}}$$

which can be further written as x = $$\sqrt[30]{5^5}$$ and y = $$\sqrt[30]{4^6}$$

As we know $$4^6 > 5^5$$

$$\Rightarrow \sqrt[30]{4^6} > \sqrt[30]{5^5} $$

$$\Rightarrow$$ y > x

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