I have no clue how to do these, and the book I have does not help at all.

Can someone help me please?

$\displaystyle (\sqrt{3} + \sqrt{5})^2$

On this one i got stuck after $\displaystyle 8+\sqrt{15}+\sqrt{15} \textcolor{red}{= 8 + 2\sqrt{15}}$

... that's all.
Multiply.$\displaystyle (\sqrt{14}+\sqrt{5})(\sqrt{14}+\sqrt{5}) \textcolor{red}{= 19 + 2\sqrt{90} = 19 + 3\sqrt{10}}$

Solve.$\displaystyle \sqrt[3] {x-7}=2$

cube both sides ...
$\displaystyle \textcolor{red}{x-7 = 8}$

$\displaystyle \textcolor{red}{x = 15}$

Solve$\displaystyle \sqrt{2x+1}=2x-5$

square both sides, then solve the resulting quadratic ... don't forget to check your results in the original equation. go ahead, try it.