Question

Represent (2+ root5 )on the real line.

Answer 1

We start by drawing equal spaced partitions on the number line to represent integers.

Using Pythagoras theorem, we know that $\sqrt 5$ is the length of hypotenuse of the triangle whose other two sides are , 1 units and 2 units. Thus we create a right angled triangle with its acute angled vertex lying at 2 on the number line. Finally, on construction of the right triangle, we use the compass and cut an arc of length $\sqrt 5$ keeping the fixed end of the compass on 2 on the number line. The point where the arc cuts the number line is $2 + \sqrt 5$ .