Approximate My Squares
Python 2, 47 ... 36 bytes

-3 bytes thanks to @JungHwanMin
-1 byte thanks to @HyperNeutrino
-2 bytes thanks to @JonathanFrech
-3 bytes thanks to @OlivierGrégoire



def f(x):s=int(x**.5);print(x/s+s)/2


Try it online!