Question

Show how√5 can be represented on the number line

Answer 1

We know that

$\sqrt{5} = \sqrt{(2)^2+(1)^2}$

Now,

Let OA be a line of length 2 unit on the number line. Now, construct AB of unit length perpendicular to OA. and join OB.

Now, in right angle triangle OAB, by Pythagoras theorem  

OB =$\sqrt{(2)^2+(1)^2}=\sqrt{5}$

Now,  take O as center and OB as radius, draw an arc intersecting number line at C.  Point C represent $\sqrt{5}$ on a number line.