Classify the following numbers as rational or irrational: (i) 2−√5 (ii) (3+√23)−√23 (iii) 2√77/√7 (iv) 1/√2 (v) 2π

Only the square roots of the square numbers, i.e. the square roots of the perfect squares are the rational numbers (i) In 2−√5, 2 is a rational number and √5 is an irrational number, then 2−√5 is a irrational number. [∵difference of a rational and an irrational number is irrational] (ii) In (3+√23)−√23 = 3+√23−√23 = 3 is a rational number (iii) 2√77/√7 = 2√11 is an irrational number (iv) In 1/√2, the number √2 is not a rational number, then 1/√2 is irrational number (v) π is an irrational number, hence 2π is an irrational number.