Represent √7 on the number line

Mark O as the origin of the line ‘l’.

Now, a perpendicular AB is drawn to OA at A with AB = 1 unit. Then,

OB² = OA² + AB²

= 1² + 1²

= 2

⇒ OB = √2 unit

An arc is drawn cutting the line at C with O as the center and OB as the radius.

Again, a perpendicular CD is drawn to OC at C with  CD = 1 unit.

⇒ OD² = OC² + CD²

= 2 + 1

= 3

⇒ OD = √3 unit

An arc is then drawn cutting the line at E with O as the center and OD as the radius.

⇒ OE = OD = √3 unit

Then, a perpendicular EF is drawn to OE at E with units and OF is joine

⇒ OF² = OE² + EF²

= 3 + 4

= 7

⇒ OD = √7 unit