Question

(18supra5radical din 3 - 12supra 4 radical din 3 - 6supra 2 radical din 3 +8 supra 2 radical din 3) - (4supra 3 radical din 2 +3supra 2 radical din 2 - 40 supra 12 radical din 2)

Answer 1

[18/(5√3)-12/(4√3)-6/(2√3)+8/(2√3)]-[4/(3√2)+3/(2√2)-40/(12√2)]= (rationalizam numitorii)
=[18√3/15-12√3/12-6√3/6+8√3/6]-[4√2/6+3√2/4-40√2/24]= (simplificam)
=[6√3/5-√3-√3+4√3/3]-[2√2/3+3√2/4-5√2/3]= (numitor comun in fiecare paranteza)
=[18√3/15-30√3/15+40√3/15]-[8√2/12+9√2/12-20√2/12]=
=28√3/15-(-3√2/12)=
=28√3/15+√2/4= (numitor comun)
=112√3/60+15√2/60=
=(15√2+112√3)/60