Question

Give an example of two irrationals whose sum is rational.​

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

Heyaa There!!

Sum of any two irrational numbers is an irrational number.

But, consider √3 and -√3. Their product is -3 and sum is 0, both of which are rational numbers.