in Quantitative Aptitude edited by
301 views
0 votes
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?

  1. $2^{\frac{1}{2}}$
  2. $3^{\frac{1}{3}}$
  3. $4^{\frac{1}{4}}$
  4. $6^{\frac{1}{6}}$
  5. $12^{\frac{1}{12}}$
in Quantitative Aptitude edited by
13.4k points
301 views

1 Answer

1 vote
1 vote

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.

11.1k points

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true