Question

square root 12 on number line​

Answer 1

1. Question⇒   square root 12 on number line​.

Step-by-step explanation:

• We can do it 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
• line.            
• Now, √3 = √(2 + 1)
• => √3 = √{(√2)2  + 12 }
• So, for representing √3 on 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

Step-by-step explanation:

The root of 12 is represented in the form of √12. Number 12 is an even number and not a prime number. Prime numbers have only two factors, 1 and the number itself, such as 1, 3, 5, etc. As we know, 12 have six factors, 1, 2, 3, 4, 6 and 12 itself, such as,

1 × 12 = 12

2 × 6 = 12

3 × 4 = 12

4 × 3 = 12

6 × 2 = 12

12 × 1 = 12

But the question comes, how can we find out the square root value of 12? First, let us write the factors of 12 as given below.

12 = 2 × 2 × 3

You can see, in the above expression, there is only one square number available on the right-hand side. Therefore, the value of the root of 12 can be written as;

Square root of 12

Taking the square term out of the root we get,

√12 = 2 √3

This is the radical form of √12. We can also write it in decimal form, by putting the value of √3 which is approximately 1.73. Hence,

√12 = 2 × 1.73

√12 = ±3.46 approximately.

Like 12, there are also many numbers which are not perfect squares. For example, 18, 20, 27, etc. are not perfect squares, as they give the value in radical form or decimal form.

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