At what height from surface of earth the value of acceleration due to gravity will fall to half that on the surface of the earth?

If g be the gravitational acceleration on the surface of earth, then gravitational acclearation at height h given as

${\text{g}}_{\text{h}}=\frac{\text{g}}{{\left(1+\frac{\text{h}}{{\mathrm{R}}_e}\right)}^2}$       

But, ${\text{g}}_{\text{h}}=\frac{\text{g}}{\text{2}}$

$\therefore \frac{\text{g}}{\text{2}}=\frac{\text{g}}{{\left(1+\frac{\text{h}}{{\mathrm{R}}_e}\right)}^2}\Rightarrow {\left(1+\frac{\text{h}}{{\mathrm{R}}_e}\right)}^2=2\Rightarrow 1+\frac{\text{h}}{{\mathrm{R}}_e}=\sqrt{2}$

$\Rightarrow \text{h}=(\sqrt{2}-1){\mathrm{R}}_e=(1.414-1)6400$

= 2649.6 km