$${\text{If }}\sqrt {1 + \frac{x}{{961}}} = \frac{{32}}{{31}}{\text{,}}$$     then the value of x is?

$$\eqalign{ & \sqrt {1 + \frac{x}{{961}}} = \frac{{32}}{{31}} \cr & \left( {{\text{Squaring both sides}}} \right) \cr & \Rightarrow 1 + \frac{x}{{961}} = \frac{{1024}}{{961}} \cr & \Rightarrow \frac{{961 + x}}{{961}} = \frac{{1024}}{{961}} \cr & \Rightarrow x = 1024 - 961 \cr & \Rightarrow x = 63 \cr} $$