Question

Give an example of two different irrational numbers whose a)sum is an irrational no. b) product is an irrational no.

Answer 1

root 3 + root 3 is 2 root 3 which is also an irrational number
root 2 into root 3 is equal to root 6 which is also a irrational number

Answer 2

Hey friend :-)

Here is your answer

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)

Hoping it helps you

Thanks :D