Question

Locate √10 and √13 on the numbers line

Answer 1

Take base 3 and height 2 and take it

Answer 2

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 .
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√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