Find the roots of the quadratic equation $x^2-4x+\sqrt{2}=0$ by the method of completing the square.

Given equation: $x^2-4x+\sqrt{2}=0$

We will try to make the left side of the equation a perfect square to get the roots easily.

Consider, $x^2-4x+\sqrt{2}=0$

${\Rightarrow x}^2-4x=-\sqrt{2}$ 

Adding $2^2$, on both sides of the given equation, we get:

${\Rightarrow x}^2-2\times \left(x\right)\times 2+2^2=-\sqrt{2}+2^2$

$\Rightarrow$ ${\left[x-2\right]}^2=-\sqrt{2}+4$

$\left[\because a^2-2ab+b^2={(a-b)}^2\right]$

$\Rightarrow$ $x-2=\pm \sqrt{4-\sqrt{2}}$  

$\Rightarrow$$x=2\pm \sqrt{4-\sqrt{2}}$

Hence, the roots of the quadratic equation $x^2-4x+\sqrt{2}=0$ are $\mathbf{2}\mathbf{\pm }\sqrt{\mathbf{4}\mathbf{-}\sqrt{\mathbf{2}}}$.