Why Mathematics is Boring (2007) [pdf](math.ucr.edu)

    # Calculate the exp root of n using a binary search
    #
    def root_binary_search(n, exp):
        # Return b, which is the exp root of n
        # b**exp should be equal to n
        #
        min = 0
        
        # For exponents < 1 the max needs to be sufficiently large
        max = n
        if exp < 1:
            while max**exp < n:
                max *= 2

        max_error = 0.00001

        while True:
            b = (max + min) / 2
            b_exp = b**exp
            error = abs(n - b_exp)
            # print(f"min: {min:15.4f}   max: {max:15.4f}   b: {b:15.4f}   b_exp: {b_exp:15.4f}   n: {n:15.4f}   error: {error:5.8f}")
            
            if error <= max_error:
                return b
            else:
                if b_exp > n:
                    max = b
                else:
                    min = b


    # Tests
    print(root_binary_search(4, 2), f"  result should be: {4**(1/2)}")
    print(root_binary_search(16, 2), f"  result should be: {16**(1/2)}")
    print(root_binary_search(5, 0.1), f"  result should be: {5**(1/0.1)}")
    print(root_binary_search(2, 10), f"  result should be: {2**(1/10)}")
    print(root_binary_search(4, 0.25), f"  result should be: {4**(1/0.25)}")

    print(root_binary_search(4, 1), f"  result should be: {4**1}")