Question

(i) Give an example of two irrationals whose sum is rational.

(ii) Give an example of two irrationals whose product is rational.

Answer 1

Hint

(i) Take ( 2 + 3–√3 ) and 2 – 3–√3 )

(ii) Take ( 2 + 2–√2 and ( 3 – 3–√3)

Sol:

(i) Let (2 +3–√3 ), ( 2 –3–√3 ) be two irrationals.

Therefore, (2 + 3–√3) + ( 2 – 3–√3) = 4 = rational number.

(ii) Let 23–√3 , 33–√3 be two irrationals.

Therefore, 23–√3 x 33–√3 = 18 = rational number.