[tex]\sqrt{45n^5}=\sqrt{9\times5n^4n}=3n^2\sqrt{5n}[/tex]
[tex]\sqrt{75}+\sqrt3=\sqrt{25\times3}+\sqrt3=5\sqrt3+\sqrt3=6\sqrt3[/tex]
(or [tex]4\sqrt3[/tex] is that = is supposed to be a minus sign)
[tex]\sqrt7(\sqrt{15}+\sqrt3)=\sqrt7(\sqrt{5\times3}+\sqrt3)=\sqrt7(\sqrt5\sqrt3+\sqrt3)=\sqrt7\sqrt3(1+\sqrt5)[/tex]
Now depending on how you want to simplify this, you could finish by writing [tex]\sqrt{21}(1+\sqrt5)[/tex] (or [tex]\sqrt{21}(-1+\sqrt5)[/tex] if that = is a minus)
