Question

Show the number $\sqrt{5}$ on the number line.

Answer 1

Draw a number line as shown in the figure. Let the point O represent 0 and point Q represent 2. Draw a perpendicular QR at Q on the number line such that QR = 1 unit. Join OR. Now, ∆OQR is a right angled triangle.
By Pythagoras theorem, we have
OR² = OQ² + QR²
= (2)² + (1)²
= 4 + 1
= 5
∴ OR = $\sqrt{5}$
Taking O as the centre and radius OR = $\sqrt{5}$, draw an arc cutting the number line at C.
Clearly, OC = OR = $\sqrt{5}$.
Hence, C represents $\sqrt{5}$ on the number line.