Question

represent root 13 on the number line

Answer 1

√13 is hypotenuse of right triangle 
using a² + b² = c² 
a² + b² = c² 
c² = (√13)² = 13 
find two square numbers whose addition is 13 
13 = 4 + 9 
= 2² + 3² 
draw line segment of either 3 or 2 units 
say 3 units 
draw perpendicular to that segment as usual 
draw arc of 2 units 
join the points to get √13 
2² + 3² = c² 
4 + 9 = c² 
c = √13