Also, can you explain why we come back to 1 and not 2. Explore round-off errors

Question

Also, can you explain why we come back to 1 and not 2.

Explore round-off errors from a large number of tn-verse operations. Maybe you have tried to hit the square root key on a calculator multiple times and then squared the number again an equal number of times. These set of inverse mathematical operations should of course bring you back to the starting value for the computations, but this does not always happen. Tb avoid tedious pressing of calculator keys we can let a computer automate the process. Here is an appropriate program: Explain with words what the program does. Then run the program. Round-off errors are here completely destroying the calculations when n is large enough! Investigate the case when we come back to 1 instead of 2 by fixing the n value and printing out r in both for loops over i.

Explanation / Answer

If u try running this code You will gwt as ..........

>>> from math import sqrt

>>> r=2

>>> for i in range(1,60):

r=sqrt(r)

print(str(i)+"th root gives "+str(r))

1th root gives 1.4142135623730951

2th root gives 1.189207115002721

3th root gives 1.0905077326652577

4th root gives 1.0442737824274138

5th root gives 1.0218971486541166

6th root gives 1.0108892860517005

7th root gives 1.0054299011128027

8th root gives 1.0027112750502025

9th root gives 1.0013547198921082

10th root gives 1.0006771306930664

11th root gives 1.0003385080526823

12th root gives 1.0001692397053021

13th root gives 1.0000846162726942

14th root gives 1.0000423072413958

15th root gives 1.0000211533969647

16th root gives 1.0000105766425498

17th root gives 1.0000052883072919

18th root gives 1.0000026441501502

19th root gives 1.0000013220742012

20th root gives 1.0000006610368821

21th root gives 1.0000003305183864

22th root gives 1.0000001652591797

23th root gives 1.0000000826295865

24th root gives 1.0000000413147925

25th root gives 1.000000020657396

26th root gives 1.000000010328698

27th root gives 1.000000005164349

28th root gives 1.0000000025821745

29th root gives 1.0000000012910872

30th root gives 1.0000000006455436

31th root gives 1.0000000003227718

32th root gives 1.0000000001613858

33th root gives 1.0000000000806928

34th root gives 1.0000000000403464

35th root gives 1.0000000000201732

36th root gives 1.0000000000100866

37th root gives 1.0000000000050433

38th root gives 1.0000000000025215

39th root gives 1.0000000000012608

40th root gives 1.0000000000006304

41th root gives 1.000000000000315

42th root gives 1.0000000000001574

43th root gives 1.0000000000000786

44th root gives 1.0000000000000393

45th root gives 1.0000000000000195

46th root gives 1.0000000000000098

47th root gives 1.0000000000000049

48th root gives 1.0000000000000024

49th root gives 1.000000000000001

50th root gives 1.0000000000000004

51th root gives 1.0000000000000002

52th root gives 1.0

53th root gives 1.0

54th root gives 1.0

55th root gives 1.0

56th root gives 1.0

57th root gives 1.0

58th root gives 1.0

59th root gives 1.0

so here what u can see is As we calculate first root we get ouput as a number which is rounded off and this process goes on so on continuing we get 59 root as 1 and hence 1 to the power 60 is then nothing but 1 .

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