Show root 12 0n number by Pythagoras theorem.
Answers
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.
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