[tex]\it a = \sqrt{(5 + 3\sqrt{3})^{2} } <=> a = |5 + 3\sqrt{3}| <=> a = 5 + 3\sqrt{3} \\ \\ b = |5 - 3\sqrt{3}| = -(5 - 3\sqrt{3}) = -5 + 3\sqrt{3} \\ \\ m_{a} = \frac{a~+~b}{2} = \frac{5 + 3\sqrt{3} - 5 + 3\sqrt{3} }{2} = \frac{6\sqrt{3} }{2} = 3\sqrt{3} \\ \\ m_{g} = \sqrt{a \cdot b} = \sqrt{(5 + 3\sqrt{3})(-5 + 3\sqrt{3})} = \sqrt{(3\sqrt{3} + 5)(3\sqrt{3} - 5) } = \sqrt{(3\sqrt{3})^{2} - 5^{2} } = \\ = \sqrt{27 - 25} = \sqrt{2}[/tex]
