Evaluate 6 + \sqrt(14) + 2 - \sqrt(9) x 2

answers are in the picture:

Hello from MrBillDoesMath!

10 - 3 sqrt(2)

Discussion:

Let f(x) =  6 + sqrt(14 + x) - sqrt(9x).  

Then

f(2) =  6 + sqrt(14 + 2) - sqrt(9*2)

      = 6 + sqrt(16) - sqrt(9*2)                 => sqrt(16) = 4

      = 6 + 4 - sqrt(9)*sqrt(2)                   => sqrt(9) = 3

      = 10 - 3 sqrt(2)

which is the first choice.

Thank you,

MrB