6.66 km/s
The velocity of a body in any given point in an orbit is
v = sqrt(u(2/r - 1/a))
where
u = Standard gravitational parameter
r = radius at which speed is to be calculated
a = length of semi-major axis
Since we're using a circular orbit, the equation can be simplified to
v = sqrt(u(2/r - 1/r)) = sqrt(u(1/r)) = sqrt(u/r)
u is the product of the body's mass and the gravitational constant.
So
u = 6.67408 x 10^-11 m^3/(kg s^2) * 5.97 x 10^24 kg
= 3.9844 x 10^14 m^3/s^2
The radius of the orbit will be the sum of earth's radius and the satellite's altitude. So
r = 6.38x10^6 m + 2.60 x 10^6 m = 8.98 x 10^6 m
Now plugging in the calculated values of u and r into the equation above gives
v = sqrt(u/r)
= sqrt(3.9844 x 10^14 m^3/s^2 / 8.98 x 10^6 m)
= sqrt(4.43697x10^7 m^2/s^2)
= 6661 m/s
= 6.661 km/s
Since we only have 3 significant figures in our data, round the result to 3 figures, giving 6.66 km/s
For orbital calculations, it's far better to be provided GM instead of M for the body being orbited. Reason is that GM is known to more accuracy than either G or M. Taking the earth for example, the value GM is known to 10 significant digits, whereas G is only known to 6 significant digits and M is known to only 5 significant digits. The reason the accuracy for GM is known so much more precisely is because of extended observations of satellites in orbit.
