#Exercise 2.19 from A primer...

from math import sqrt

for n in range(1,60):
    r = 2.0
    for i in range(n):
        r = sqrt(r)
    for i in range(n):
        r = r**2
    print(f'{n} times sqrt and **2: {r}')



"""
Terminal> python repeated_sqrt.py
1 times sqrt and **2: 2.0000000000000004
2 times sqrt and **2: 1.9999999999999996
3 times sqrt and **2: 1.9999999999999996
4 times sqrt and **2: 1.9999999999999964
5 times sqrt and **2: 1.9999999999999964
6 times sqrt and **2: 1.9999999999999964
7 times sqrt and **2: 1.9999999999999714
8 times sqrt and **2: 2.0000000000000235
9 times sqrt and **2: 2.0000000000000235
...
40 times sqrt and **2: 1.9999360966436217
41 times sqrt and **2: 1.9994478907329654
42 times sqrt and **2: 1.9984718365144798
43 times sqrt and **2: 1.9965211562778555
44 times sqrt and **2: 1.9965211562778555
45 times sqrt and **2: 1.9887374575497223
46 times sqrt and **2: 1.9887374575497223
47 times sqrt and **2: 1.9887374575497223
48 times sqrt and **2: 1.9887374575497223
49 times sqrt and **2: 1.8682459487159784
50 times sqrt and **2: 1.6487212645509468
51 times sqrt and **2: 1.6487212645509468
52 times sqrt and **2: 1.0
53 times sqrt and **2: 1.0
54 times sqrt and **2: 1.0
55 times sqrt and **2: 1.0
56 times sqrt and **2: 1.0
57 times sqrt and **2: 1.0
58 times sqrt and **2: 1.0
59 times sqrt and **2: 1.0
"""