[tex]\displaystyle \\
\sqrt{2^4}+ \sqrt{ \frac{5}{0,0(2)}}+ \sqrt{ \frac{55}{0,0(02)}}+ \sqrt{ \frac{555}{0,0(002)}} = \\ \\ \\
=\sqrt{16}+ \sqrt{ \frac{5}{ \frac{2}{90} }}+ \sqrt{ \frac{55}{ \frac{2}{990}}}+ \sqrt{ \frac{555}{ \frac{2}{9990} }} = \\ \\ \\
=\sqrt{16}+ \sqrt{ \frac{5 \times 90}{ 2 }}+ \sqrt{ \frac{55\times 990}{ 2}}+ \sqrt{ \frac{555\times 9990}{ 2}} = [/tex]
[tex]\displaystyle \\
=\sqrt{16}+ \sqrt{ 5 \times 45}+ \sqrt{ 55\times 495}+ \sqrt{555\times4995} = \\ \\
=\sqrt{16}+ \sqrt{ 225}+ \sqrt{ 27225}+ \sqrt{2772225} = \\ \\
=4+15+ 165+ 1665 = 1849 = 43 \times 43 = \boxed{43^2 = pp}
[/tex]
