A quote from "Python Programming: An Introduction to Computer Science"
We could have taken the square root using exponentiation **. Using math.sqrt is somewhat more efficient.
"Somewhat", but to what extent, and how?
Theoretically, hammar's answer and duffymo's answer are good guesses. But in practice, on my machine, it's not more efficient:
>>> import timeit
>>> timeit.timeit(stmt='[n ** 0.5 for n in range(100)]', setup='import math', number=10000)
0.15518403053283691
>>> timeit.timeit(stmt='[math.sqrt(n) for n in range(100)]', setup='import math', number=10000)
0.17707490921020508
Part of the problem is the . operation. If you import sqrt directly into the namespace, you get a slight improvement.
>>> timeit.timeit(stmt='[sqrt(n) for n in range(100)]', setup='from math import sqrt', number=10000)
0.15312695503234863
Key word there: slight.
Further testing indicates that as the number gets larger, the benefit you get from using sqrt increases. But still not by a lot!
>>> timeit.timeit(stmt='[n ** 0.5 for n in range(1000000)]', setup='import math', number=1)
0.18888211250305176
>>> timeit.timeit(stmt='[math.sqrt(n) for n in range(1000000)]', setup='import math', number=1)
0.18425297737121582
>>> timeit.timeit(stmt='[sqrt(n) for n in range(1000000)]', setup='from math import sqrt', number=1)
0.1571958065032959