If $\sqrt{2}$ is a root of the equation $kx^2 + \sqrt{2}x - 4 = 0$, find the value of k.

Since $\sqrt{2}$ is a root of the equation $kx^2 + \sqrt{2}x - 4 = 0$, $x = \sqrt{2}$ satisfies the given equation.

Substituting $x = \sqrt{2}$ in the given equation:

$k ( \sqrt{2} )^2 + \sqrt{2} \times \sqrt{2} - 4 = 0 \\[0.5em] \Rightarrow 2k + 2 - 4 = 0 \\[0.5em] \Rightarrow 2k - 2 = 0 \\[0.5em] \Rightarrow 2k = 2 \\[0.5em] \Rightarrow k = 1$

Hence, the value of k is 1