How do I calculate new minimal speed for a glider when I put water into the tank? Lets say a glider weights 400kg and has a minimal speed of 70km/h.

When it has additionally 100l water, so in total 500kg, what is the new minimal speed?

I would argue, that in order to reach the same point in the polar diagram, we have to scale according to

$v_2 = v_1 \cdot \sqrt{m_2/m_1}$

because drag and lift forces scale quadratic with speed.

The result would be 78km/h.

However, in the theory we learn

$v_2 = v_1 \cdot m_2/m_1 = 87km/h$

Q: Isn't that wrong?
$v_2 = v_1 \cdot \sqrt{m_2/m_1}$ is the correct formula.

$v_2 = v_1 \cdot m_2/m_1 = 87km/h$ is simply wrong, possible that it is only a typing mistake, but it is wrong just the same.