Question

example of problem that adding an irrational no to rational gives sometimes rational

Answer 1

Two irrational numbers whose
(1) sum is rational r
10+2√5 and 5-2√5

To check:

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)


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