Question

Locate $\sqrt{17}$ on the number line.

Answer 1

Here,$17=4^2+1$
So, draw a right angled $\Delta OAB$, in which OA = 4 units and AB = 1 unit and $\angle OAB={90}^{\circ }$
By using Pythagoras theorem, we get
$OB=\sqrt{O{A}^2+A{B}^2}=\sqrt{4^2+1^2}=\sqrt{16+1}=\sqrt{17}$

Taking $OB=\sqrt{17}$ as radius and point O as centre, draw an arc which meets the number line at point P on the positive side of it. The point P represents $\sqrt{17}$ on the number line.