Question

Which is greater--- 2^1/2 or 3^1/3. Answer with a detailed explanation.

Answer 1

LCM of 2,3 = 6.

(1) 2^1/2

$= \ \textgreater \ (2^ \frac{1}{2} )^6$

$= \ \textgreater \ 2 ^{ \frac{6}{2} }$

$= \ \textgreater \ 2^3$

= > 8.


(2) 

3^1/3

$= \ \textgreater \ (3^{\frac{1}{3} } )^6$

$= \ \textgreater \ 3^ \frac{6}{3}$

$= \ \textgreater \ 3^2$

= > 9.


Therefore 3^1/3 is greater than 2^1/2.


Hope this helps!

Answer 2

Hi,

Please see the attached file!


Thanks