Question

Find the mean proportion between $$(\sqrt{26} - \sqrt{17})$$ and $$(\sqrt{26} + \sqrt{17})$$.

Answer 1

The mean proportion between two numbers $$a$$ and $$b$$ is given by $$\sqrt{ab}$$.

$$\sqrt{(\sqrt{26} - \sqrt{17})(\sqrt{26} + \sqrt{17})} = \sqrt{(\sqrt{26})^2 - (\sqrt{17})^2}$$ 

$$= \sqrt{26 - 17}$$

$$= \sqrt{9}$$

$$= 3$$