(c) 10-3
\(\sqrt{1369} +\sqrt{0.0615+X}\) = 37.25
\(\Rightarrow\) \(\sqrt{0.0615+X}\) = 37.25 - \(\sqrt{1369}\)
= 37.25 - 37 = 0.25
\(\Rightarrow\) 0.0615 + x = (0.25)2 = 0.0625
\(\Rightarrow\) x = 0.0625 - 0.0615 = 0.001 = \(\frac{1}{10^3}\) = 10-3.