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Show how square root 5 can be represented on the number line.

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

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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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