Explanation

Let $\upsilon \propto \sigma^{a}\rho^{b}\lambda^{c}$ Equating dimensions on both sides, $\left\lbrack M^{0}L^{1}T^{- 1} \right\rbrack \propto \left\lbrack MT^{- 2} \right\rbrack^{a}\left\lbrack ML^{- 3} \right\rbrack^{b}\lbrack L\rbrack^{c}$ $\propto \lbrack M\rbrack^{a + b}\lbrack L\rbrack^{- 3b + c}\lbrack T\rbrack^{- 2a}$ Equating the powers of $M,\ L,\ T$ on both sides, we get $a + b = 0$ $- 3b + c = 1$ $- 2a = - 1$ Solving, we get $a = \frac{1}{2}\ ,\ b = - \frac{1}{2}\ ,\ c = - \frac{1}{2}$ $\therefore\ \upsilon \propto \sigma^{1/2}\ \rho^{- 1/2}\ \lambda^{- 1/2}$ $\therefore\ \upsilon^{2} \propto \frac{\sigma}{\rho\lambda}$