Question : The smallest among $\sqrt[6]{12}, \sqrt[3]{4}, \sqrt[4]{5}, \sqrt{3}$ is:
Option 1: $\sqrt[6]{12}$
Option 2: $\sqrt[3]{4}$
Option 3: $\sqrt{3}$
Option 4: $\sqrt[4]{5}$

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Question : $\frac{1}{3 - \sqrt{8}} - \frac{1}{\sqrt{8} - \sqrt{7}} + \frac{1}{\sqrt{7} - \sqrt{6}} - \frac{1}{\sqrt{6} - \sqrt{5}} + \frac{1}{\sqrt{5} - 2} = ?$
Option 1: 5
Option 2: 4
Option 3: 3
Option 4: 2

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Answer 1

Correct Answer: $\sqrt[4]{5}$

Solution : Given: $\sqrt[6]{12}, \sqrt[3]{4}, \sqrt[4]{5}, \sqrt{3}$
LCM of 6, 3, 4, 2 is 12.
$\sqrt[6]{12} \Rightarrow {(12^{\frac{1}{6}})}^{12} = 12^{2} = 144$
$\sqrt[3]{4} \Rightarrow {(4^{\frac{1}{3}})}^{12} = 4^{4} = 256$
$\sqrt[4]{5} \Rightarrow {(5^{\frac{1}{4}})}^{12} = 5^{3} = 125$
$\sqrt{3} \Rightarrow {(3^{\frac{1}{2}})}^{12} = 3^{6} = 729$
125 is the smallest of these numbers.
Hence, the correct answer is $\sqrt[4]{5}$ .

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Question : The smallest among 126,43,54,3 is:Option 1: 126Option 2: 43Option 3: 3Option 4: 54

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Question : The smallest among $\sqrt[6]{12}, \sqrt[3]{4}, \sqrt[4]{5}, \sqrt{3}$ is:
Option 1: $\sqrt[6]{12}$
Option 2: $\sqrt[3]{4}$
Option 3: $\sqrt{3}$
Option 4: $\sqrt[4]{5}$