Number Systems — Question 3

Representing $\sqrt{5}$ as the sum of squares of two natural numbers:

5 = 4 + 1 = (2)² + (1)²

Let l be the number line. If point O represents number 0 and point A represents number 2 then draw a line segment OA = 2 units.

At A, draw AC ⊥ OA. From AC, cut off AB = 1 unit.

We observe that OAB is a right angled triangle at A. By Pythagoras theorem, we get:

(OB)² = (OA)² + (AB)²

(OB)² = (2)² + (1)²

(OB)² = 4 + 1

(OB)² = 5

OB = $\sqrt{5}$ units

With O as centre and radius = OB, we draw an arc of a circle to meet the number line l at point P.

As, OP = OB = $\sqrt{5}$ units, the point P will represent the number $\sqrt{5}$ on the number line as shown in the figure below: