Question

Represent √ 5 on the number line.

Answer 1

1) Draw number line as shown in the above mentioned attachment.

2) Let, the point 0 represent 0 and point A represent 2 .

3) Draw perpendicular AX at A on the number line and cut-off arc AB = 1 unit.

4) We have OA = 2 units and AB = 1 unit.

5) Using Pythagoras theorem, we have

OB² = OA² + AB²

OB² = (2)² + (1)²

OB² = 4 + 1

OB² = 5

OB = √5

6) Taking O as the centre and OB = √5 as radius .

7) Draw an arc cutting real line at C.

OC = OB = √5

8) Hence, C represents √5 on the number line.