Question

Represent root 10 and 3 on a no line

Answer 1

Answer:

here is your answer with diagrams

Answer 2

Answer:

To represent the √10 on the line first draw the right angle triangle in the       xy-plane such that base on the x-axis and one end of triangle in on origin of plane and perpendicular is not on y-axis

lengths of sides are following

Base = b = 3

perpendicular = p = 1

Then by pathegorus theorem

h² = p² + b² = 3² + 1² = 9 + 1 = 10

h² = 10

h = √10

Now with the help of compass draw the arc of √10 on the line as shown in the first figure.

To represent the √3 on the line first draw the right angle triangle in the       xy-plane such that base on the x-axis and one end of triangle in on origin of plane and perpendicular is not on y-axis

lengths of sides are following

Base = b = √2

perpendicular = p = 1

Then by pathegorus theorem

h² = p² + b² = √2² + 1² = 2 + 1 = 3

h² = 3

h = √3

Now with the help of compass draw the arc of  length √3 on the line as shown in the second figure.

Note: In the second figure we draw first another triangle of base and perpendicular of  size 1 units to find the √2 on the line then use that √2 as the base for required construction of √3