What is the mean proportional between $2.5$ and $0.625$?

The mean proportional between two numbers $a$ and $b$ is given by the formula $\sqrt{ab}$.
Here, $a=2.5$ and $b=0.625$.
$$\text{Mean Proportional}=\sqrt{2.5\times 0.625}$$
$$\text{Mean Proportional}=\sqrt{\frac{25}{10}\times \frac{625}{1000}}=\sqrt{\frac{15625}{10000}}$$

We know that $\sqrt{15625}=125$ and $\sqrt{10000}=100$.
$$\text{Mean Proportional}=\frac{125}{100}=1.25$$