c
(c) Let \(\sqrt {3 + \sqrt 5 } = \sqrt x + \sqrt y \)

\(3 + \sqrt 5 = \,x + y + 2\sqrt {xy} \). Obviously \(x + y = 3\)

and \(4xy = 5\). So \({(x - y)^2} = 9 - 5 = 4\) or \((x - y) = 2\)

After solving \(x = {5 \over 2},y = {1 \over 2}\).

Hence, \(\sqrt {3 + \sqrt 5 } = \sqrt {{5 \over 2}} + \sqrt {{1 \over 2}} = {{\sqrt 5 + 1} \over {\sqrt 2 }}\).