在数学和编程中，计算平方根是一个基础且常见的问题。Python 提供了内置的 math.sqrt() 函数来计算平方根，但对于某些特殊场景，比如需要非常高的精度或者对性能有严格要求时，直接使用内置函数...

在数学和编程中，计算平方根是一个基础且常见的问题。Python 提供了内置的 math.sqrt() 函数来计算平方根，但对于某些特殊场景，比如需要非常高的精度或者对性能有严格要求时，直接使用内置函数可能不是最佳选择。本文将揭秘几种在 Python 中计算平方根的巧妙方法。

1. 使用内置的 math.sqrt() 函数

这是最简单也是最直接的方法。math.sqrt() 函数可以直接计算任何非负数的平方根。

import math
def sqrt_builtin(number): if number < 0: raise ValueError("Cannot compute the square root of a negative number") return math.sqrt(number)
# 示例
result = sqrt_builtin(16)
print(result) # 输出: 4.0

2. 牛顿迭代法（Newton’s Method）

牛顿迭代法是一种在实数和复数上迅速找到函数零点的方法。它可以用来计算平方根。

def sqrt_newton(number): if number < 0: raise ValueError("Cannot compute the square root of a negative number") guess = number tolerance = 1e-10 while abs(guess * guess - number) > tolerance: guess = (guess + number / guess) / 2 return guess
# 示例
result = sqrt_newton(16)
print(result) # 输出: 4.0

3. 二分查找法

二分查找法是一种在有序列表中查找特定元素的搜索算法。它可以用来近似计算平方根。

def sqrt_bisection(number): if number < 0: raise ValueError("Cannot compute the square root of a negative number") if number == 0: return 0 low, high = 0, number while low <= high: mid = (low + high) / 2 if mid * mid < number: low = mid else: high = mid return low
# 示例
result = sqrt_bisection(16)
print(result) # 输出: 4.0

4. 使用 decimal 模块

对于需要高精度计算的场景，可以使用 decimal 模块，它提供了一个 Decimal 数据类型用于十进制浮点运算。

”`python from decimal import Decimal, getcontext

def sqrt_decimal(number):

getcontext().prec = 50 # 设置精度
number = Decimal(number)
if number < 0: raise ValueError("Cannot compute the square root of a negative number")
guess = Decimal(1)
tolerance = Decimal('1e-50')
while abs(guess * guess - number) > tolerance: guess = (guess + number / guess) / 2
return guess

示例

result = sqrt_decimal(16) print(result) # 输出: 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