Between two distinct irrational numbers there lie______rational numbers.

State true or false: (i) Between any two distinct integers there is always an integer. (ii) Between any two distinct rational numbers there is always a rational number. (iii) Between any two distinct rational numbers there are infinitely many rational numbers.

Find two rational and two irrational numbers between the rational numbers (5)/(7) and (9)/(11) .

Write any two irrational numbers whose product is rational number.

Are there two distinct irrational numbers such that their difference is a rational number? Justify

Are there two distinct irrational numbers such that their difference is a rational number? Justify.

Find two irrational numbers such that their sum is a rational number. Can you find two irrational numbers whose product is a rational number.

Give an example of two irrational numbers whose difference is a rational number.

(a) (i) By taking any two irrational numbers, prove that their sum is a rational number. (ii) By taking any two irrational numbers, prove that their difference is a rational number. (b) Insert in between 1/7 and 2/7 (i) a rational number : (ii) an irrational number.