Which of the following is true?
$$\eqalign{ & {\text{I}}.\root 3 \of {11} > \sqrt 7 > \root 4 \of {45} \cr & {\text{II}}.\sqrt 7 > \root 3 \of {11} > \root 4 \of {45} \cr & {\text{III}}.\sqrt 7 > \root 4 \of {45} > \root 3 \of {11} \cr & {\text{IV}}.\root 4 \of {45} > \sqrt 7 > \root 3 \of {11} \cr} $$

Solution (By Examveda Team)

$$\eqalign{ & \root 3 \of {11} ,\,\sqrt 7 ,\,\root 4 \of {45} \cr & {11^{\frac{1}{3}}},\,{7^{\frac{1}{2}}},\,{45^{\frac{1}{4}}} \cr & {\text{Take LCM of 3, 2, 4 is 12}} \cr & {11^4},\,{7^6},\,{45^3} \cr & {\text{14641,}}\,{\text{117649,}}\,{\text{91125}} \cr & 117649 > 91125 > 14641 \cr & {\text{Option C is true}} \cr & \sqrt 7 > \root 4 \of {45} > \root 3 \of {11} \cr} $$