Question

Sum of two irrational numbers whose sum is rational example

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)