Question

represent root 10.5 on the number line

Answer 1

Draw a line AB of10.5 units

Extend the line making BC = 1unit, and AC = 11.5 units

Take the midpoint of AC as M = 11.5/2 = 5.75

Draw a semi-circle from A to C as M as the centre.

Draw a line perpendicular to AC at point C until is intersects and bisects with the semicircle forming a new point called D

CD=√10.5

Put your compass needle at point M and then the other end at point D.

Draw an arc till it reaches the number line or intersects with the number line and the point formed let's call it D2(or any other thing you like)

D=D2=√10.5