Question

i just need to know if these are already simplified or not

Answer 1

ANSWER:

$\begin{gathered} \frac{3+\sqrt{3}}{\:3}\rightarrow\text{ Yes} \\ \\ \frac{2+\sqrt{3}}{\:3}\rightarrow\text{ Yes} \\ \\ \frac{2+2\sqrt{3}}{4}\rightarrow\text{ No} \\ \\ \frac{1+\sqrt{2}}{\:4}\rightarrow\text{ Yes} \end{gathered}$

STEP-BY-STEP EXPLANATION:

We analyze each case to determine if it can be simplified further, like so:

$\begin{gathered} \frac{3+\sqrt{3}}{\:3}\rightarrow\text{ It's already simplify} \\ \\ \frac{2+\sqrt{3}}{\:3}\rightarrow\text{ It's already simplify} \\ \\ \frac{2+2\sqrt{3}}{4}=\frac{2\left(1+\sqrt{3}\right)}{4}=\frac{1+\sqrt{3}}{2}\rightarrow\text{ it's not simplified} \\ \\ \frac{1+\sqrt{2}}{\:4}\rightarrow\text{ It's already simplify} \end{gathered}$