How do I print a list of the first 1000 (Square Roots, Cube Roots, Fourth Roots, and Fifth Roots) in Python?

Question

I am curious on how to generate my own list (the first, nth number) of: (Square Roots, Cube Roots, Fourth Roots, and Fifth Roots) in Python.

Something like this (Without GUI):

I am really curious on how this is created, because I would learn a lot about Roots in math in general, and about solving Python Root Problems.

Thank you.

Answer 1

As you are more interested in various different powers you could write a function which takes Nth number you want to print up to and the power you want to use. It will then return a tuple of the current value of n, the value of n to the power and then a text formula.

The function also yields the results so if you were looking for large values of N they wouldnt all be loaded into memory immediately.

In this example i have then loaded the pandas module just for easy printing of the output as a data frame.

EDIT updated with an example for roots. the roots function can take an optional parameter for decimal precision since roots most often return decimal values. if no precision value is gien to the function the full precision will be shown

import pandas as pd

def get_nth_powers(nth, power):
    for n in range(nth):
        written_formula = (" x ".join([str(n)] * power))
        yield (n, n ** power, written_formula)


def get_nth_roots(nth, root, decimal_precision=0):
    decimal_precision = f'0.{decimal_precision}f' if decimal_precision else ''
    for n in range(nth):
        value = n ** (1/root)
        written_formula = (" x ".join([f'{value:{decimal_precision}}'] * root))
        yield (n, value, written_formula)


data = get_nth_powers(1000, 4)
df = pd.DataFrame(data, columns=('Nth', 'To Power', 'formula'))
print(df)

data = get_nth_roots(1000, 2, 3)
df = pd.DataFrame(data, columns=('Nth', 'value', 'formula'))
print(df)

OUTPUT

     Nth      To Power                formula
0      0             0          0 x 0 x 0 x 0
1      1             1          1 x 1 x 1 x 1
2      2            16          2 x 2 x 2 x 2
3      3            81          3 x 3 x 3 x 3
4      4           256          4 x 4 x 4 x 4
..   ...           ...                    ...
995  995  980149500625  995 x 995 x 995 x 995
996  996  984095744256  996 x 996 x 996 x 996
997  997  988053892081  997 x 997 x 997 x 997
998  998  992023968016  998 x 998 x 998 x 998
999  999  996005996001  999 x 999 x 999 x 999

[1000 rows x 3 columns]
     Nth      value          formula
0      0   0.000000    0.000 x 0.000
1      1   1.000000    1.000 x 1.000
2      2   1.414214    1.414 x 1.414
3      3   1.732051    1.732 x 1.732
4      4   2.000000    2.000 x 2.000
..   ...        ...              ...
995  995  31.543621  31.544 x 31.544
996  996  31.559468  31.559 x 31.559
997  997  31.575307  31.575 x 31.575
998  998  31.591138  31.591 x 31.591
999  999  31.606961  31.607 x 31.607

[1000 rows x 3 columns]