Let's check every one of them:
[tex]\sqrt[]{4}+\sqrt[]{16}=2+4=6,\text{ it's not irrational}[/tex][tex]\sqrt[]{5}+\sqrt[]{36}=\sqrt[]{5}+6,\text{ it is irrational}[/tex][tex]\sqrt[]{9}+\sqrt[]{24}=3+\sqrt[]{24},\text{ it is irrational}[/tex][tex]2\cdot\sqrt[]{4}=2\cdot2=4,\text{ it is not irrational}[/tex][tex]\sqrt[]{49}\cdot\sqrt[]{81}=7\cdot9=63,\text{ it is not irrational}[/tex][tex]3\cdot\sqrt[]{12}=6\sqrt[]{3},\text{ it is irrational}[/tex]
