Question

GIVE AN EXAMPLE OF 2 IRRATIONAL NUMBERS WHOSE PRODUCT IS RATIONAL ?

Answer 1

Heya !!!

Here is Your Answer.

(4 + √5) and (4 - √5)
They are irrational.
But their product....

(4+√5)(4-√5)
= 4² - 5
= 11

And,
2√2 and 3√2

= 2√2 × 3√2
= 6×2 = 12

Hope It Helps

Answer 2

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