Project Euler Problem 80-高精度开方-牛顿逼近法
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..., 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.
这个题涉及到高精度开方，像python，haskell等语言原生支持高精度小数，做这个题不成问题，直接使用api即可。我习惯用java，研究BigDecimal发现里面没有开方的方法，所以需要手动实现。可以采用牛顿逼近法解决开方问题，可以用BigDecimal实现高精度。牛顿逼近法参见：http://baike.baidu.com/view/1514354.htm
