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 $