Question

Represent `sqrt(3)` on the number line.

Answer 1

Given: Represent `sqrt(3)` on the number line.

Stepwise calculation:

1. Start with a number line and mark the point O as 0 and the point A as 1 unit from O.

2. Draw a perpendicular line from A and cut off a length AB = 1 unit on this perpendicular.

3. Join OB. Using the Pythagoras theorem in ΔOAB: 

`OB = sqrt(OA^2 + AB^2)`

`OB = sqrt(1^2 + 1^2)`

`OB = sqrt(2)`

So, B represents `sqrt(2)` on this construction.

4. From point B on the number line, draw a perpendicular line and cut off a length BC = 1 unit on it.

5. Join OC. Using the Pythagoras theorem in ΔOBC: 

`OC = sqrt(OB^2 + BC^2)`

`OC = sqrt((sqrt(2))^2 + 1^2)`

`OC = sqrt(2 + 1)`

`OC = sqrt(3)`

6. Draw an arc with center O and radius OC to intersect the number line at D.

7. The point D on the number line represents `sqrt(3)`.