To locate √10 on number line follow the steps. let 3cm = 1 unit
1] √10 = √3²+1²
2]draw a number line OC such that OA=AB=OC=1 unit
3] draw a perpendicular line from C of 1 unit [as √10 = √3²+1² ] and name the point as C
4] join O and C it will form a triangle
by pythagoras theorem
OC = √10
now taking the radius of OC in compass draw an arc touching the number line .
and that point will be √10 .