9. CBQ - Finding simplest form of rationals

The teacher asked a student to expand ${(\sqrt{5}+\sqrt{14})}^2$. The teacher also provided a hint to use an algebraic expression to solve it. The student actively involved in solving it.

 

1. What is the expanded form of ${(\sqrt{5}+\sqrt{14})}^2$?

 

2. What is the simplified form of ${(\sqrt{5}+\sqrt{14})}^2$?

 

3. Is the simplified form rational or irrational?

 

4. If the expression was ${\left(\sqrt{5}-\sqrt{3}\right)}^2$, what would the simplest form be?