Find the fourth proportional to 3a, 6a² and 2ab²

Let fourth proportional to 3a, 6a² and 2ab² be x

$\Rightarrow 3a : 6a^2 = 2ab^2 : x \\[1em] \Rightarrow \dfrac{3a}{6a^2} = \dfrac{2ab^2}{x} \\[1em] \Rightarrow x = \dfrac{2ab^2 \times 6a^2}{3a} \\[1em] \Rightarrow x = 4a^2b^2$

Hence, fourth proportional to 3a, 6a² and 2ab² is 4a²b².