Answer
The escape speed is 4.34 km/s
Work Step by Step
We can use the equation for escape speed to find the escape speed at a height of 36,000 km above the earth's surface. Note that at this height, the distance $R$ from the center of the earth is 42,380 km.
$v_{esc} = \sqrt{\frac{2~G~M}{R}}$
$v_{esc} = \sqrt{\frac{(2)(6.67\times 10^{-11}~m^3/kg~s^2)(5.98\times 10^{24}~kg)}{4.238\times 10^7~m}}$
$v_{esc} = 4.34\times 10^3 ~m/s$
$v_{esc} = 4.34~km/s$
The escape speed is 4.34 km/s.