Question

root(4+root7)-root(4-root7)

Answer 1

let y = root(4 + root 7) - root (4 - root 7)
then y^2 = ( root(4 + root 7) - root (4 - root 7))^2 (by using (a+b)^2 = a^2 + b^2 + 2ab

    y^2 = 4 + root7 + 4 - root 7 - 2 (root(4+ root7)(root (4 - root 7))
           = 8 - 2(root (16 - 7)     ( (a+b) (a-b) = a^2 - b^2)
           = 8 - 2 * 3                     ( root 9 = 3)
           = 8 - 6
          =  2
    y   = root 2