Dimension of wavelength $\lambda$ is $L$

Dimension of acceleration due to gravity $g$ is $LT ^{-2}$

Dimension of Density of water $p$ is $ML ^{-3}$

Let $v \propto \lambda^{ a } g ^{ b } \rho^{ c }$

Using Dimensional method

$a+b-3 c=1$

$c =0$

$-2 b =-1$

$b =0.5$

Hence, $a =0.5$

$\therefore v \propto \sqrt{ g \lambda}$

$v ^{2} \propto g \lambda$