## It is well known that if the square root of a natural number is not an integer, then it is irrational. The decimal expansion of such square roots is infinite without any repeating pattern at all.

The square root of two is $1.41421356237309504880\cdots$, and the digital sum of the first one hundred decimal digits is $475$.

For the first one hundred natural numbers, find the total of the digital sums of the first one hundred decimal digits for all the irrational square roots.

### To find the total of the digital sums of the first one hundred decimal digits for all the irrational square roots of the first one hundred natural numbers, you can follow these steps:

1. Import the math module in Python to access mathematical functions and constants.

“`python

import math

“`

2. Initialize a variable `total_sum` to keep track of the total sum of the digital sums.

“`python

total_sum = 0

“`

3. Iterate over the range of natural numbers from 1 to 100 using a for loop.

“`python

for number in range(1, 101):

“`

4. Use the `math.sqrt()` function to calculate the square root of `number`.

“`python

square_root = math.sqrt(number)

“`

5. Check if the square root is an integer using the `is_integer()` method of a float. If it is an integer, continue to the next iteration of the loop.

“`python

if square_root.is_integer():

continue

“`

6. Convert the square root to a string and remove the decimal point.

“`python

decimal_digits = str(square_root).replace(“.”, “”)

“`

7. Extract the first one hundred decimal digits by slicing the string.

“`python

decimal_digits = decimal_digits[:100]

“`

8. Calculate the sum of the individual digits by converting each character back to an integer using the `int()` function and summing them using the `sum()` function.

“`python

digit_sum = sum(int(digit) for digit in decimal_digits)

“`

9. Add the digit sum to the `total_sum` variable.

“`python

total_sum += digit_sum

“`

10. After the loop completes, print the final `total_sum`.

“`python

print(total_sum)

“`

Here is the complete code:

“`python

import math

total_sum = 0

for number in range(1, 101):

square_root = math.sqrt(number)

if square_root.is_integer():

continue

decimal_digits = str(square_root).replace(“.”, “”)

decimal_digits = decimal_digits[:100]

digit_sum = sum(int(digit) for digit in decimal_digits)

total_sum += digit_sum

print(total_sum)

“`

The output of this code will be the total of the digital sums of the first one hundred decimal digits for all the irrational square roots of the first one hundred natural numbers.

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