Question

Show root 12 0n number by Pythagoras theorem. ​

Answer 1

We can do it by using Pythagoras Theorem.

We can write √12 = √(9 + 3)

=> √12 = √{32 + (√3)2 }      

So, for representing √12 on a number line, first, we have to represent √3 on number  line.            

Now, √3 = √(2 + 1)

=> √3 = √{(√2)2  + 12 }

So, for representing √3 on a number line, first, we have to represent √2 on number  line.            

Now, √2 = √(1 + 1)

=> √2 = √(12  + 12 )

Construction:

1. Take a line segment OA = 1 unit on the x-axis.   (consider 1 unit = 1cm)    

2. Draw a perpendicular on A and draw a line OB = 1 unit  

3. Now join OB with √2

4. Take O as center and OB as radius, draw an arc which cuts the x-axis at point E.

5. Hence, the line segment OE represents √2

6. Now, draw a perpendicular on B and draw a line BC = 1 unit

7. Now join OC with √3

8. Take O as center and OC as radius, draw an arc which cuts the x-axis at point F.

9. Hence, the line segment OF represents √3

10. Now, draw a perpendicular on C and draw a line CD = 3 unit

11. Now join OD with √12

12. Take O as center and OD as radius, draw an arc which cuts the x-axis at point G.

13. Hence, the line segment OG represents √12

So, in this way, we represent √12 on the number line.

Answer 2

by using Pythagoras Theorem.

We can write √12 = √(9 + 3) => √12 = √{32 + (√3)2 } So, for representing √12 on number line, first we have to represent √3 on number