The non-negative real numbers x ,y and z satisfy the two equations

x^2 + y^2 + z^2 = 9

xy + yz + zx = 6

What is the sum of x, y, and z?

x^2 + y^2 + z^2 + 2(xy + yz + zx) = (x + y + z) ^2

= 21 = (x + y + z)^2

x + y + z = sqrt(21)

(Make sure you know why it's positive sqrt(21)!)