Question

Arrange these numbers in ascending order
$\sqrt{2},6^{\frac{1}{6}},3^{\frac{1}{3}}$

• A. 2^1/2, 3^1/3, 6^1/6
• B. 6^1/6 , 2^1/2, 3^1/3
• C. 2^1/2, 6^1/6, 3^1/3
• D. 6^1/6, 3^1/3, 2^1/2

Answer 1

The correct option is B

6^1/6 , 2^1/2, 3^1/3

Since the base of the number is positive, equalities will remain same if we multiply same number to the powers.
For such type of question, we should find the LCM of the base terms.
The LCM of 2, 3 and 6 is 12.
$2^{\frac{12}{2}},3^{\frac{12}{3}},6^{\frac{12}{6}}\Rightarrow 2^6=64,3^4=81,6^2=36\Rightarrow 2^6=64,3^4=81,6^2=36$
So, ascending order is: 36, 64, 81
Terms corresponding to the above pattern =$6^{\frac{1}{6}}<2^{\frac{1}{2}}<3^{\frac{1}{3}}$