51 lines
1.3 KiB
Python
51 lines
1.3 KiB
Python
#!/usr/bin/python
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# It is well known that if the square root of a natural number is not an integer, then it is irrational.
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# The decimal expansion of such square roots is infinite without any repeating pattern at all.
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#
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# The square root of two is 1.41421356237309504880..., and the digital sum of the first one hundred decimal digits is 475.
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#
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# For the first one hundred natural numbers, find the total of the digital sums of the first one hundred decimal digits
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# for all the irrational square roots
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from timeit import default_timer
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from mpmath import sqrt, mp
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def is_square(n):
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p = sqrt(n)
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m = int(p)
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return bool(p == m)
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def main():
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start = default_timer()
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# Set the precision to 100 digits
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mp.dps = 102
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sum_ = 0
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for i in range(2, 100):
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if not is_square(i):
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# Calculate the square root of the current number with the given precision
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# and sum the digits to the total.
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root = str(sqrt(i))
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sum_ = sum_ + int(root[0])
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for j in range(2, 101):
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sum_ = sum_ + int(root[j])
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end = default_timer()
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print('Project Euler, Problem 80')
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print(f'Answer: {sum_}')
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print(f'Elapsed time: {end - start:.9f} seconds')
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if __name__ == '__main__':
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main()
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