The method is absolutely correct.We have,

Orbital velocity V is given by V²=GM/R where R=r+h=15,400km

Putting G=6.67X10^-11 and M=6X10²⁴ S.I units,we get,

V²=6.67X10^-11X6X10²⁴/154X10⁵=(6.67X3/77)X10⁸.

Since you want the exact answer,I calculated using calculator and got the exact answer as 5097.74m/s.But my method will be like this,

6.67X3=(20/3)(3)=20 and (20/77)(10⁸)=(2000/77)(10⁶).Now,2000/7 is approximately 26.

So,V²=26X10⁶ V=5.1X10³=5100.(as rt26 is app. 5.1).

Hence,the answer I got is V=5100m/s.