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Which value among $$\root 4 \of 7 ,\,\root 3 \of {11} $$ and $$\root {12} \of {1257} $$ is the largest?
Answer & Solution
Correct Answer:
Option
A
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 $$\root 3 \of {11} $$
$$\root 4 \of 7 ,\,\root 3 \of {11} $$ 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 $$\root 3 \of {11} $$
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