Question

Show how √5 can be represented on the number line.

Answer 1

Step-by-step explanation:

Step 1: On the number line, take 2 units from O and represent the point as A. Step 2: At point A, draw a perpendicular and mark B such that AB = 1 unit. Step 3: Now, with O as the center and OB as radius, draw an arc to cut the number line at C. Step 4: Point C represents √5 on the number line.

Answer 2

Here, to locate $\sqrt{5}$

Draw, a right angle $\triangle ABC$ in which AC = 2 units and AB =1 unit

and $\angle CAB=90^0$

By Pythagoras theorem, we get,

$BC=\sqrt{AC^2+AB^2 }\\= \sqrt{2^2+1^1} \\=\sqrt{4+1} \\=\sqrt{5}$

• Taking, BC =$\sqrt{5}$ as a radius and C as the centre, draw an arc that meets the number line at point P on the positive side of it.
• It is clear that point P represents $\sqrt{5}$ on the number line.