1
(5-2√6)(3+√6)√(√2+√3)²=(5-2√6)(3+√6)*(√2+√3)=
(15+5√6-6√6-12)(√2+√3)=(3-√6)(√2+√3)=3√2+3√3-2√3-3√2=√3
2
4/(7-3√5)-[√15(√3-√5)/√5(√5-√3)]²=4/(7-3√5)-(-√3)²=4/(7-3√5)-3=
=(4-21+9√5)/(7-3√5)=(9√5-17)/(7-3√5)=(9-√5-17)(9√5+17)/(7-3√5)(9√5+1)=
=(405-289)/(63√5+119-135-51√5)=116/(12√5-16)=116/[4(3√5-4)=29/(3√5-4)