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