# 3. Show how $\sqrt{5}$ can be represented on the number line.

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

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