Question

Are there two irrational numbers whose sum and product both are rationals ? Justify

Answer 1

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.

Answer 2

yes there are number which are irrational and their products is rational 
example : 
⇒ √2 × √8 
⇒ √16 
⇒ 4 
∴ the product of two irrational is a rational 
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yes in some cases the sum of two irrational numbers is rational 
example :
⇒ √5 + ( - √5 )
⇒ √5 - √5 
⇒ 0 
∴ the sum of irrational numbers is rational