Question

how to represent root 10 on number line?

Answer 1

Consider a number line. Let the point O represent 0 and point A represent 3.Now draw a perpendicular AP at A on the number line and cut off arc AB = 1 unit.Using Pythagoras Theorem, we have
OB(square) = OA(square) + AB(square)
= OB(square) = (3)square + (1)square 
= OB(square) = 10
OB = root10
With O as the centre and  as radius draw an arc cutting real line at C. Clearly, OC = OB = root10
Thus, C represents root10 on number line..

Answer 2

Answer:

We can do it by using Pythagoras Theorem.  

We can write   √10  as follows:

√10  =  √9+1

​⇒  √10  = √3 ^2  + 1 ^2

       

The construction steps are as follows:

1. Take a line segment AO=3 unit on the x-axis.   (consider 1 unit = 2 cm)    

2. Draw a perpendicular on O and draw a line OC=1 unit  

3. Now join AC with √ 10 .  

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

5. The line segment AC in the below diagram represents   10  units.

Step-by-step explanation: