Square root by guessing

You can trap $\sqrt{7}$ between two numbers and halve the gap again and again. After $30$ halvings the trap is far narrower than a millionth.

The idea. Start with $2 < \sqrt{7} < 3$. Try the middle. If its square is below $7$, the root is in the upper half; if not, it is in the lower half.

Your tasks.

1. In middle, return the number halfway between lo and hi.
2. In step, return the new pair (lo, hi) that still holds the root of n.
3. Set root to the middle of the trap after $30$ steps for $n = 7$, starting from (2, 3).