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1. Which among $2^{\frac{1}{2}}$ , $3^{\frac{1}{3}}$ , $4^{\frac{1}{4}}$ , $6^{\frac{1}{6}}$ and $12^{\frac{1}{12}}$ is largest?

A. $2^{\frac{1}{2}}$

B. $3^{\frac{1}{3}}$

C. $4^{\frac{1}{4}}$

D. $12^{\frac{1}{12}}$

Solution:

LCM in power 2, 3, 4, 6, 12 is 12
We multiplied the LCM to the power of the numbers.

2^{\frac{1 \times 12}{2}}, 3^{\frac{1 \times 12}{3}}, 4^{\frac{1 \times 12}{4}}, 6^{\frac{1 \times 12}{6}} and 12^{\frac{1 \times 12}{12}}

We get,
= 2⁶, 3⁴, 4³, 6², 12
= 64, 84, 64, 36, 12
Hence, greatest number would be

3^{\frac{1}{3}}

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