Answer
$\frac{(2\sqrt {15}+3\sqrt {5})}{120}$
Work Step by Step
Step 1: $\frac{2+\sqrt 3}{8\sqrt {15}}$
Step 2: Rationalize the denominator: $\frac{2+\sqrt 3}{8\sqrt {15}}\times\frac{8\sqrt {15}}{8\sqrt {15}}$.
Step 3: $\frac{2(8\sqrt {15})+8\sqrt {15}(\sqrt 3)}{8\sqrt {15}\times8\sqrt {15}}$
Step 4: $\frac{16\sqrt {15}+8\sqrt {15\times3}}{64(15)}$
Step 5: $\frac{16\sqrt {15}+8\sqrt {15\times3}}{64(15)}$
Step 6: $\frac{16\sqrt {15}+8\sqrt {9\times5}}{64(15)}$
Step 7: $\frac{16\sqrt {15}+8(3)\sqrt {5}}{64(15)}$
Step 8: $\frac{8(2\sqrt {15}+3\sqrt {5})}{64(15)}$
Step 9: $\frac{1(2\sqrt {15}+3\sqrt {5})}{8(15)}$
Step 10: $\frac{(2\sqrt {15}+3\sqrt {5})}{120}$
