Represent the numbers √5 and √10 on a number line.

By Pythagoras theorem,

(√5)² = 2² + 1²

⇒ (√5)² = 4 + 1

First mark 0 and 2 on the number line. Then, draw a perpendicular of 1 unit from 2. And Join the top of perpendicular and 0. This line would be equal to √5. Now measure the line with compass and marc an arc on the number line with the same measurement. This point is √5.

Also,

By Pythagoras theorem,

(√10)² = 3² + 1²

⇒ (√10)² = 9 + 1

First mark 0 and 3 on the number line. Then, draw a perpendicular of 1 unit from 3. And Join the top of perpendicular and 0. This line would be equal to √10. Now measure the line with compass and marc an arc on the number line with the same measurement. This point is √10.