Verified answer

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1)

√10+√6 ? √11+√5

(√10+√6)² ? (√11+√5)²

10+2*√10*√6+6 ? 11+2*√11*√5+5

16+2*√60>16+2*√55.

2)

2+√11 ? √5+√10

(2+√11)² ? (√5+√10)²

4+2*2*√11 +11 ? 5+2*√5*√10+10

15+2*√(4*11) ? 15+2*√50

15+2*√44<15+2*√50.