Question : Which of the following is TRUE? I. $\sqrt[3]{11}>\sqrt{7}>\sqrt[4]{45}$ II. $\sqrt{7}>\sqrt[3]{11}>\sqrt[4]{45}$ III. $\sqrt{7}>\sqrt[4]{45}>\sqrt[3]{11}$ IV. $\sqrt[4]{45}>\sqrt{7}>\sqrt[3]{11}$
Option 1: Only I
Option 2: Only II
Option 3: Only III
Option 4: Only IV
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Correct Answer: Only III
Solution : LCM of 3, 2, and 4 is 12. After taking the 12 th power, $\sqrt[3]{11}$ → $11^4=14641$ $\sqrt{7}→7^6→49^3=117649$ $\sqrt[4]{45}→45^3=91125$ Comparing the above three terms, we can conclude that $\sqrt{7}>\sqrt[4]{45}>\sqrt[3]{11}$ Hence, the correct answer is 'Only III'.
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