已知 sqrt (2)约等于 1.414，要求不用数学库，求 sqrt (2)精确到小数（python开发）

1.二分法

E = 0.0000000001
def sqrt2():
    low = 1.4
    high = 1.5
    mid = (low + high) / 2

    while high - low > E:
        if mid * mid > 2:
            high = mid
        else:
            low = mid
        mid = (high + low) / 2
    print(mid)
sqrt2()

2.牛顿迭代法

E = 0.1 ** 10
def sqrt2(x):
    if abs(x ** 2 - 2) > E:
        x = (sqrt2(x - (x ** 2 -2) / (2 * x)))
    else:
        x
    return x