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

(N/A) To represent $\sqrt{10}$ on the number line,we use the Pythagorean theorem: $a^2 + b^2 = c^2$.
We can write $10$ as $3^2 + 1^2 = 10$,so $\sqrt{10} = \sqrt{3^2 + 1^2}$.
Step $1$: Draw a number line and mark a point $O$ at $0$ and a point $A$ at $3$ units from $O$.
Step $2$: At point $A$,construct a perpendicular line segment $AB$ of length $1$ unit.
Step $3$: Join $O$ and $B$. By the Pythagorean theorem,the length of $OB$ is $\sqrt{3^2 + 1^2} = \sqrt{10}$.
Step $4$: With $O$ as the center and $OB$ as the radius,draw an arc that intersects the number line at point $P$.
The point $P$ represents $\sqrt{10}$ on the number line.