0
votes

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

- $2^{\frac{1}{2}}$
- $3^{\frac{1}{3}}$
- $4^{\frac{1}{4}}$
- $6^{\frac{1}{6}}$
- $12^{\frac{1}{12}}$

See all

Dark Mode

0
votes

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

- $2^{\frac{1}{2}}$
- $3^{\frac{1}{3}}$
- $4^{\frac{1}{4}}$
- $6^{\frac{1}{6}}$
- $12^{\frac{1}{12}}$

See all

1
votes

Here the bases of numbers can't be made same so making their powers equal

1. $2^{\frac{1}{2}} = 2^{({6})\frac{1}{12}} = 64^{\frac{1}{12}}$

2. $3^{\frac{1}{3}} = 3^{({4})\frac{1}{12}} = 81^{\frac{1}{12}}$

3. $4^{\frac{1}{4}} = 4^{({3})\frac{1}{12}} = 64^{\frac{1}{12}}$

4. $6^{\frac{1}{6}} = 6^{({2})\frac{1}{12}} = 36^{\frac{1}{12}}$

5. $12^{\frac{1}{12}}$

Here clearly we can see $3^{\frac{1}{3}} = 3^{({4})\frac{1}{12}} = 81^{\frac{1}{12}}$ is the Largest value.

Hence** (B) $3^{\frac{1}{3}}$** is the Answer.

See all