Answer:
[tex]\large\boxed{\sqrt{24}+\sqrt{25}-\sqrt{54}=5-\sqrt6}[/tex]
Step-by-step explanation:
[tex]\text{Use}\\\\\sqrt{a}=b\iff b^2=a\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}[/tex]
[tex]\sqrt{24}+\sqrt{25}-\sqrt{54}\\\\\sqrt{24}=\sqrt{4\cdot6}=\sqrt4\cdot\sqrt6=2\sqrt6\\\sqrt{25}=5\\\sqrt{54}=\sqrt{9\cdot6}=\sqrt9\cdot\sqrt6=3\sqrt6\\\\\sqrt4=2\ because\ 2^2=4\\\sqrt{25}=5\ because\ 5^2=25\\\sqrt9=3\ because\ 3^2=9\\\\\sqrt{24}+\sqrt{25}-\sqrt{54}=2\sqrt6+5-3\sqrt6=5+(2\sqrt6-3\sqrt6)=5-1\sqrt6[/tex]
