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
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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