a)
(7√3+√48-√75)*√3= (7√3+√(16*3)-√(25*3)*√3 = (7√3+4√3-5√3)*√3= 6√3*√3= 6*3=18
b)
(6-√5)(2+7√5)= 12+42√5-2√5-√5*7√5 = 12+40√5-7*5= 40√5+12-35= =40√5-23
c)
(5√2+6√3)(6√2-5√3)= 5√2*6√2 – 5√2*5√3 +6√3*6√2 -6√3*6√3 =
=30*2 – 25√6+36√6 – 30*3= 60+11√6 -90= 11√6-30
d)
(√17-√11)(√17+√11) = 17-11 =6
e)
(2√x-5√y)(2√x+5√y)=4x-25y
f)
(√6-2)² = 6-√6 +4=10-√6
g)
(3√7-2√3)²= 9*7-12√21+4*3 = 63-12√21 +12= 75-12√21