Question

one example of rational number and an irrational number whose sum is irrational and product is rational

Answer 1

exmple of two irrational numbers whose sum is rational

Give exmple of two irrational numbers whose-

i) Sum is rational

ii) Product is rational

iii) Quotient is rational

Two irrational numbers whose
 (i) sum is rational are
10 + 2√5 and 5 - 2√5 
Checking:
Sum of these two irrational numbers = 10 + 2√5 and 5 - 2√5 = 15 (a rational number)

(ii)  product is rational are
10 + 2√5 and 10 - 2√5 
Checking:
Product of these two irrational numbers
                    = (10 + 2√5) (10 - 2√5)
                    = (10)2 -  (2√5)2 
                    = 100 - 20 = 80 (a rational number)
(iii)  quotient is rational are
                 10√5 and 5√5 
Checking:
Quotient of these two irrational numbers = 
                 (10√5)/(5√5) = 2 (a rational number)