Question

what is root 5 ,represent in number line

Answer 1

Please refer to the diagrams.

Since we know that 2² + 1² = 5, we can draw horizontal line (1 unit long) at 2 on the number line. (as shown in first diagram)

The dotted line (in diagram 2), the horizontal line we drew and the number line will then form a right angled triangle. Using Pythagoras' theorem, we know that the length of the hypotenuse (the dotted line) is $\sqrt{5}$.

Using a compass, you can then measure the length of $\sqrt{5}$ and using the point 0 as the origin to turn alongside the direction of the arrow in diagram 3.

Then you can find the point $\sqrt{5}$ in diagram 4.