Q.3. Show how can be represented on the number line.

Solution:

We can write 5 = 4 + 1 = (2)2 + (1)2

So we will construct a right angled triangle with sides 2 and 1 and the hypotenuse will be the required measure of $\sqrt{5}$.

1. Let AB be a line of length 2 unit on number line.

2. At B, draw a perpendicular line BC of length 1 unit. Join CA.

3. Now, ABC is a right angled triangle.

Applying Pythagoras theorem,

AB2 + BC2 = CA2

⇒ 22 + 12 = CA2

⇒ CA2 = 5

⇒ CA = $\sqrt{5}$

Thus, CA is a line of length $\sqrt{5}$ unit.

4. Taking CA as a radius and A as a centre draw an arc cutting the number line at D. Now AD = AC = $\sqrt{5}$, because they are the radii of the same circle.