Consider the following recursive iteration scheme for different values of variable $P$ with the initial guess $x_{1} =1$: $$x_{n + 1} = \frac{1}{2}\left ( x_{n} + \frac{P}{x_{n}} \right ), \:\:\:n = 1, 2, 3, 4, 5$$ For $P = 2$, $x_{5}$ is obtained to be $1.414$, rounded-off to three decimal places. For $P = 3$, $x_{5}$ is obtained to be $1.732$, rounded-off to three decimal places.

If $P = 10$, the numerical value of $x_{5}$ is ___________________. *(round off to three decimal places)*