(i) 2− √5

In the given number 2 is rational number and √5 is irrational number. So, √5 is subtracted from 2. Now subtracting we will get an irrational number.

Hence, 2− √5 is an irrational number.

(ii) (3+ √23)− √23 = 3+ √23− √23 = 3 which is a rational number

(iii) 2√7/ 7√7 = 2/7 which is a rational number

(iv) 1/√2

is irrational number.

Because the quotient of a non-zero rational number with an irrational number is irrational.

(v) 2π

2 is rational number and π is an irrational number. So, we know that the product of a nonzero rational number with an irrational number is irrational.

Hence, 2π is irrational number.