Answer
$\frac{(4\sqrt {10}+5\sqrt {2})}{70}$
Work Step by Step
Step 1: $\frac{4+\sqrt 5}{7\sqrt {10}}$
Step 2: Rationalize the denominator: $\frac{4+\sqrt 5}{7\sqrt {10}}\times\frac{7\sqrt {10}}{7\sqrt {10}}$.
Step 3: $\frac{4(7\sqrt {10})+7\sqrt {10}(\sqrt 5)}{7\sqrt {10}\times7\sqrt {10}}$
Step 4: $\frac{28\sqrt {10}+7\sqrt {10\times5}}{49(10)}$
Step 5: $\frac{28\sqrt {10}+7\sqrt {25\times2}}{49(10)}$
Step 6: $\frac{28\sqrt {10}+7(5)\sqrt {2}}{49(10)}$
Step 8: $\frac{7(4\sqrt {10}+5\sqrt {2})}{49(10)}$
Step 9: $\frac{1(4\sqrt {10}+5\sqrt {2})}{7(10)}$
Step 10: $\frac{(4\sqrt {10}+5\sqrt {2})}{70}$