The equation of current in terms of the peak value of current in sinusoidal form is, $i=i_0\sin \left(\omega t+\varphi \right)$, the given $i-t$ equation can be written as, $$\begin{gathered} \mathit{\text{i}}=\sqrt{5}\times 2\times \sqrt{2}\left(\frac{2}{\sqrt{5}\times 2\times \sqrt{2}}\text{sin}\omega \mathit{\text{t}}+\frac{6}{\sqrt{5}\times 2\times \sqrt{2}}\text{cos}\omega \mathit{\text{t}}\right) \\ \Rightarrow \mathit{\text{i}}=\sqrt{5}\times 2\times \sqrt{2}\left(\frac{2}{\sqrt{10}}\text{sin}\omega \mathit{\text{t}}+\frac{3}{\sqrt{10}}\text{cos}\omega \mathit{\text{t}}\right) \end{gathered}$$ ${\mathit{\text{⇒i}}}_0=\sqrt{5}\times 2\times \sqrt{2} A$, the relation between root mean square and peak current is, ${\mathit{\text{i}}}_{\text{rms}}=\frac{{\mathit{\text{i}}}_0}{\sqrt{2}}=2\sqrt{5} \text{A}$.