Question

give an example of two irrational numbers whose sum and product both are rationals

Answer 1

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)

Answer 2

Answer:

Normally, sum of any two irrational numbers is an irrational number. However, consider √2 and -√2. Their product is -2 and sum is 0, both of which are rational numbers. Thus, there can be numbers whose sum and product both are rationals.

Step-by-step explanation: