Question

Represent $\sqrt{10}$ on the number line.

Answer 1

Given $\sqrt{10}=\sqrt{3^2+1}$
We use Pythagoras formula to represent the given value on the number line.
Construction:
1. Take a line segment $AO=3$ units on x-axis.
2. Draw a perpendicular on O and draw line $OC=1$ unit.
3. Now join AC with $\sqrt{10}$
4. Take $A$ as centre and $AC$ as radius, draw an arc which cuts the x-axis at point $E$.
5. Thus, the line segment $AE$ represents $\sqrt{10}$