Question

Compare : `sqrt24 and root(3)(35)`

Answer 1

`sqrt24 = (24)^(1/2) and root(3)(35) = 35^(1/3)`
L.C.M. of 2 and 3 is 6.

`1/2 xx 3/3 = 3/6, 1/3 xx 2/2 = 2/6`

⇒ `24^(1/2) = 24^(3/6) = (24^3)^(1/6) = ( 13824 )^(1/6)`

⇒ `35^(1/3) = 35^(2/6) = (35^2)^(1/6) = (1225)^(1/6)`

⇒ 13824 > 1225

⇒ `13824^(1/6) > root(3)(35)` 
⇒ `sqrt24 > root(3)(35)`