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)

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