j sqrt (5+2sqrt (6))+sqrt (8-2sqrt (15))

To simplify the expression $\sqrt{5+2\sqrt{6}} + \sqrt{8-2\sqrt{15}}$, we can use the following steps:<br /><br />1. Simplify each square root term separately.<br /><br />For the first term, $\sqrt{5+2\sqrt{6}}$:<br />We can rewrite it as $\sqrt{(\sqrt{6} + 1)^2}$, which simplifies to $\sqrt{6} + 1$.<br /><br />For the second term, $\sqrt{8-2\sqrt{15}}$:<br />We can rewrite it as $\sqrt{(\sqrt{5} - \sqrt{3})^2}$, which simplifies to $\sqrt{5} - \sqrt{3}$.<br /><br />2. Combine the simplified terms.<br /><br />$\sqrt{5+2\sqrt{6}} + \sqrt{8-2\sqrt{15}} = (\sqrt{6} + 1) + (\sqrt{5} - \sqrt{3})$<br /><br />3. Simplify the expression further.<br /><br />$(\sqrt{6} + 1) + (\sqrt{5} - \sqrt{3}) = \sqrt{6} + \sqrt{5} - \sqrt{3} + 1$<br /><br />Therefore, the simplified expression is $\sqrt{6} + \sqrt{5} - \sqrt{3} + 1$.