**Understanding the Problem:**

We are given that a balloon is rising from rest with a constant acceleration of g/8. We need to find the time taken by a stone released from the balloon to reach the ground when it has risen to a height h.

**Solution:**

To solve this problem, we need to analyze the motion of the balloon and the stone.

**Motion of the Balloon:**

Let's consider the motion of the balloon first. The balloon is rising with a constant acceleration of g/8, which means the acceleration is in the upward direction. Since the balloon is rising, its initial velocity is zero.

Using the second equation of motion, we can determine the time taken by the balloon to reach a height h.

h = (1/2) * a * t^2

Here, h is the height reached by the balloon, a is the acceleration, and t is the time taken.

Simplifying the equation, we get:

h = (1/2) * (g/8) * t^2
2h = (g/8) * t^2
t^2 = (16h)/g

Taking the square root of both sides, we get:

t = sqrt(16h/g) = 4 * sqrt(h/g)

**Motion of the Stone:**

Now, let's consider the motion of the stone. The stone is released from the balloon when it has reached a height h. It will then fall freely under the influence of gravity.

The time taken by the stone to reach the ground can be determined using the equation:

h = (1/2) * g * t^2

Here, h is the height from which the stone is released, g is the acceleration due to gravity, and t is the time taken.

Simplifying the equation, we get:

h = (1/2) * g * t^2
2h = g * t^2
t^2 = (2h)/g

Taking the square root of both sides, we get:

t = sqrt(2h/g)

**Comparing the Results:**

Comparing the time taken by the balloon and the stone, we find:

t_balloon = 4 * sqrt(h/g)
t_stone = sqrt(2h/g)

Substituting the given values, we have:

t_balloon = 4 * sqrt(h/g)
t_stone = sqrt(2h/g)

Taking the ratio of these two times:

t_balloon / t_stone = (4 * sqrt(h/g)) / sqrt(2h/g)
= 4 * sqrt(h/g) * (1/sqrt(2h/g))
= 4 * (sqrt(h/g) * (1/sqrt(2h/g)))
= 4 * (1/sqrt(2))

Simplifying further, we get:

t_balloon / t_stone = 4/sqrt(2)
= 4 * (1/√2)
= 4/√2
= 2√2

Therefore, the time taken by the stone to reach the ground when released from a balloon that has risen to height h is 2√h/g.

**Conclusion:**

The time taken by the stone to reach the ground when released from a balloon that has risen to height h is 2√h/g.