Implemented Square Root Algorithm (TheAlgorithms#1687)

* Added to maths and strings

* added changes suggest by cclauss

* added square root function

* Fixed type hinting

* fixed type error

* Fixed another type error

Author: coleman2246

maths/square_root.py

@@ -0,0 +1,63 @@
+import math
+
+
+def fx(x: float, a: float) -> float:
+    return math.pow(x, 2) - a
+
+
+def fx_derivative(x: float) -> float:
+    return 2 * x
+
+
+def get_initial_point(a: float) -> float:
+    start = 2.0
+
+    while start <= a:
+        start = math.pow(start, 2)
+
+    return start
+
+
+def square_root_iterative(
+    a: float, max_iter: int = 9999, tolerance: float = 0.00000000000001
+) -> float:
+    """
+    Sqaure root is aproximated using Newtons method.
+    https://en.wikipedia.org/wiki/Newton%27s_method
+    
+    >>> all(abs(square_root_iterative(i)-math.sqrt(i)) <= .00000000000001  for i in range(0, 500))
+    True
+    
+    >>> square_root_iterative(-1)
+    Traceback (most recent call last):
+        ...
+    ValueError: math domain error
+
+    >>> square_root_iterative(4)
+    2.0
+
+    >>> square_root_iterative(3.2)
+    1.788854381999832
+
+    >>> square_root_iterative(140)
+    11.832159566199232
+    """
+
+    if a < 0:
+        raise ValueError("math domain error")
+
+    value = get_initial_point(a)
+
+    for i in range(max_iter):
+        prev_value = value
+        value = value - fx(value, a) / fx_derivative(value)
+        if abs(prev_value - value) < tolerance:
+            return value
+
+    return value
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()