(1)5√28-9√1/3-1/3√63+√12
=5*√4*√7-9*(√3)/3-(√7*√9)/3+√3*√4
=10√7-3√3-√7+2√3
=10√7-√7+2√3-3√3
=9√7-√3
(2)(√12-√0.5)-(√75-√18)
=[√3√4-(√2)/2]-(√25*√3-√9√2)
=[2√3-(√2)/2]-(5√3-3√2)
=2√3-5√3-(√2)/2+3√2
=(2-5)√3+(3-1/2)√2
=-3√3+(5√2)/2
(3)5/6√18÷2√8×1/3√54
=5/6*3√2/(4√2)*1/3*3√6
=(5√2)/2/(4√2)*√6
=(5√2)/(4√2)/2*√6
=5/8*√6=(5√6)/8
(4)(√3+2)²(7-4√3)
=(3+4√3+4)(7-4√3)
=(7+4√3)(7-4√3)
=7²-(4√3)²
=49-48=1
(5)(√2+1)^2012(√2-1)
=(√2+1)^2011*(√2+1)*(√2-1)
=(√2+1)^2011*(2-1)
=(√2+1)^2011