Question

evaluate : [(5+2*square root 6)square root]+[(8-2*square root 15)square root]

Answer 1

$$\begin{gathered} \sqrt{5+2\sqrt{6}}+\sqrt{8-2\sqrt{15}} \\ =\sqrt{3+2+2\sqrt{3}.\sqrt{2}}+\sqrt{5+3-2\sqrt{5}.\sqrt{3}} \\ =\sqrt{{\left(\sqrt{3}\right)}^2+{\left(\sqrt{2}\right)}^2+2\left(\sqrt{3}\right)\left(\sqrt{2}\right)}+\sqrt{{\left(\sqrt{5}\right)}^2+{\left(\sqrt{3}\right)}^2-2\left(\sqrt{5}\right)\left(\sqrt{3}\right)} \\ =\sqrt{{\left(\sqrt{3}+\sqrt{2}\right)}^2}+\sqrt{{\left(\sqrt{5}-\sqrt{3}\right)}^2} \\ =\sqrt{3}+\sqrt{2}+\sqrt{5}-\sqrt{3} \\ =\sqrt{2}+\sqrt{5} \end{gathered}$$