Which value among $$\root 4 \of 7 ,\,\root 3 \of {11} $$   and $$\root {12} \of {1257} $$  is the largest?

A. $$\root 3 \of {11} $$

B. $$\root 4 \of 7 $$

C. $$\root {12} \of {1257} $$

D. All are equal

Answer: Option A

Solution(By Examveda Team)

Given,
$$\root 4 \of 7 ,\,\root 3 \of {11} $$   and $$\root {12} \of {1257} $$
Take LCM of 4, 3 and 12 = 12
$${\left( 7 \right)^{\frac{1}{4}}},\,{\left( {11} \right)^{\frac{1}{3}}},\,{\left( {1257} \right)^{\frac{1}{{12}}}}$$
Multiplying the power by 12 = 7³, 11⁴, 1257
i.e., 343, 14641, 1257
Therefore, from above greater one is $$\root 3 \of {11} $$