b
(b) \({E_1} = \frac{1}{2}K{x^2}\)

\(\Rightarrow x = \sqrt {\frac{{2{E_1}}}{K}} \),

\({E_2} = \frac{1}{2}K{y^2}\)

\(\Rightarrow y = \sqrt {\frac{{2{E_2}}}{K}} \) and

\(E = \frac{1}{2}K{(x + y)^2} \)

\(\Rightarrow x + y = \sqrt {\frac{{2E}}{K}} \)

\( \Rightarrow \sqrt {\frac{{2{E_1}}}{K}} + \sqrt {\frac{{2{E_2}}}{K}} = \sqrt {\frac{{2E}}{K}} \)

\( \Rightarrow \sqrt {{E_1}} + \sqrt {{E_2}} = \sqrt E \)