Expand and simplify (3 + 4*root5)(3 - 2*root5)

Using FOIL to expand the brackets we get

9 - 6root5 + 12root5 + 8*root5^2

Square rooting then squaring a number cancels out, so we are left with 8*5 or 40 for the last term.

Simplify to give

9 + 6*root5 + 40

6*root5 + 49