

"""simple docstring"""






import math



def   lowercase_	(    _lowercase       :		float							,      _lowercase       :		float	):




					'''simple docstring'''






					if (
					    not isinstance(_lowercase							,      (int, float)	)
					    or power_factor < -1
					    or power_factor > 1
					):
										raise ValueError("power_factor must be a valid float value between -1 and 1."	)
					return apparent_power * power_factor



def   lowercase_	(    _lowercase       :		float							,      _lowercase       :		float	):




					'''simple docstring'''






					if (
					    not isinstance(_lowercase							,      (int, float)	)
					    or power_factor < -1
					    or power_factor > 1
					):
										raise ValueError("power_factor must be a valid float value between -1 and 1."	)
					return apparent_power * math.sqrt(1 - power_factor**2	)


if __name__ == "__main__":
	import doctest

	doctest.testmod()





"""simple docstring"""






import math



def   lowercase_	(    _lowercase       :		int	):




					'''simple docstring'''






					return math.sqrt(_lowercase	) * math.sqrt(_lowercase	) == num



def   lowercase_	(    _lowercase       :		int	):




					'''simple docstring'''






					UpperCAmelCase			:   List[Any]      =				0
					UpperCAmelCase			:   Tuple      =				n
					while left <= right:
										UpperCAmelCase			:   Tuple      =				(left + right) // 2
										if mid**2 == n:
															return True
										elif mid**2 > n:
															UpperCAmelCase			:   List[str]      =				mid - 1
										else:
															UpperCAmelCase			:   Any      =				mid + 1
					return False


if __name__ == "__main__":
	import doctest

	doctest.testmod()


