If $$x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } .... \propto $$      then the value of x is?

Solution (By Examveda Team)

$$\eqalign{ & x = \sqrt {a\root 3 \of {ab\sqrt {a\root 3 \of {ab} } } } ....... \propto \cr & {\text{Square both sides}} \cr & {x^2} = a\root 3 \of {abx} {\text{ }}\left( {\therefore \sqrt {a\root 3 \of {ab} } .... \propto } \right) \cr & {\text{Again cube both sides}} \cr & {x^6} = {a^3}abx \cr & {x^5} = {a^4}b \cr & x = \root 5 \of {{a^4}b} \cr} $$