[tex](3\sqrt2+2\sqrt5)^2 = (3\sqrt2)^2+2\cdot 3\sqrt2\cdot 2\sqrt5+(2\sqrt5)^2 = \\ \\ = 9\cdot 2+12\sqrt{10}+4\cdot 5 = 18+20+12\sqrt{10} = 38+12\sqrt{10}[/tex]
[tex](3\sqrt5+1)^3 = (3\sqrt5)^3 +3\cdot (3\sqrt5)^2\cdot 1+3\cdot 3\sqrt5\cdot 1^2+1^3 = \\ \\ = (3\sqrt5)^2\cdot (3\sqrt5)+3\cdot 9\cdot 5+9\sqrt5+1 = \\ \\ = 9\cdot 5\cdot 3\sqrt5+135+9\sqrt5+1 = \\ \\ = 136+135\sqrt5+9\sqrt5 = \\ \\ = 136+144\sqrt5[/tex]
