Question:
By geometrical construction, it is possible to divide a line segment in the ratio $\sqrt{3}: \frac{1}{\sqrt{3}}$
Solution:
True
Given, ratio $=\sqrt{3}: \frac{1}{\sqrt{3}}$
$\therefore \quad$ Required ratio $=3: 1 \quad$ [multiply $\sqrt{3}$ in each term]
So, $\sqrt{3}: \frac{1}{\sqrt{3}}$ can be simplified as $3: 1$ and 3 as well as 1 both are positive integer.
Hence, the geometrical constrution is possible to divide a line segment in the ratio 3 : 1