[tex]\begin{gathered} 9 - 4\sqrt{5} \\ \\ = 4 + 5 - 4\sqrt{5} \\ \\ = (- 2)^2 + (\sqrt{5})^2 + (2 \times - 2 \times \sqrt{5}) \\ \\ = (- 2 + \sqrt{5})^2 \\ \\ = (\sqrt{5} - 2)^2 \\ \\ \\ \therefore \sqrt{9 - 4\sqrt{5}} = \sqrt{5} - 2 \end{gathered}[/tex]
Hope this may be helpful.
