Question

find the pari of irrational number such that their sum is rational number

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

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).

hope it helps you friend.

@ sk