Question

show that the sum and product of two rational numbers (5+root 3) and (5-root3) are rational numbers

Answer 1

the sum of (5 + root 3) and (5 - root 3)
   = 5 + root 3 + 5 - root 3
  = 10  ( since +root 3 and -root 3 get cancelled due to opposite sign)
The product of (5 + root 3) and (5 - root 3)
   = (5 + root 3)  (5 - root 3)  = 5^2 - (root 3)^2
   =   25 - 3
   =   22

Note: (using identity formula )
(a+b)(a-b) =   a^2 - b^2