Question : The smallest among $\sqrt[6]{12},\sqrt[3]{4},\sqrt[4]{5},\sqrt3$ is:
Option 1: $\sqrt[6]{12}$
Option 2: $\sqrt[3]{4}$
Option 3: $\sqrt3$
Option 4: $\sqrt[4]{5}$
Correct Answer: $\sqrt[4]{5}$
Solution : Given: $\sqrt[6]{12},\sqrt[3]{4},\sqrt[4]{5},\sqrt3$ LCM of 6, 3, 4, 2 is 12. $\sqrt[6]{12} ⇒ \left (12^\frac{1}{6} \right )^{12} = 12^2 = 144$ $\sqrt[3]{4} ⇒ \left (4^\frac{1}{3} \right )^{12} = 4^4 = 256$ $\sqrt[4]{5} ⇒ \left (5^\frac{1}{4} \right )^{12} = 5^3 = 125$ $\sqrt{3} ⇒ \left (3^\frac{1}{2} \right )^{12} = 3^6 = 729$ 125 is the smallest of these numbers. Hence, the correct answer is $\sqrt[4]{5}$.
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