Revisiting Irrational Numbers

Carrom originated in India and became popular throughout the World after World War 1. Although carrom boards come in different sizes, the official size is a square of 74 cm. A carrom set of 19 coins (or carrom men) has 1 red coin (queen), 9 black and 9 white coins. Official pieces must have a diameter between 3.02 - 3.18 cm, thickness between 7 - 9 mm thick, and mass between 5.0 - 5.5 g. A round striker is used to strike the coins with the aim of putting them in the four circular corner pockets. At the beginning of the game all the 19 coins are placed within a circlular area at the middle of the board.

Do you know how many irrational numbers are linked to carrom? Find some of them and share in the discussion board below.

And, if your school does not have a carrom team, it’s time for you to take the lead.

EXERCISE: Prove that $\sqrt{5}$ is an irrational number.

SELF PRACTICE: Prove that these are irrational numbers:
i) $\sqrt{7}$
ii) $\sqrt{12}$
iii) $\sqrt{11}$

EXERCISE: Prove that $3+2&space;\sqrt{5}$ is an irrational number.

SELF PRACTICE: Prove that the following are irrational numbers:
i) $5+3&space;\sqrt{2}$
ii) $4+5&space;\sqrt{7}$
iii) $12-8&space;\sqrt{3}$

EXERCISE: Prove that $\frac{1}{\sqrt{2}}$ is an irrational number.

EXERCISE: Prove that $7&space;\sqrt{5}$ is an irrational number.

EXERCISE: Prove that $6+{\sqrt{2}}$ is an irrational number.

SELF PRACTICE: Prove that the following are irrational numbers:
i) $\frac{1}{\sqrt{5}}$
ii) $11&space;\sqrt{7}$
iii) $9+{\sqrt{8}}$

Discussion