The problem asks to combine the expression $5\sqrt{8} + \sqrt{50}$ and simplify it.

1. Problem Description

The problem asks to combine the expression $5\sqrt{8} + \sqrt{50}$ and simplify it.

2. Solution Steps

First, we simplify the radicals individually.

$\sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}$

$\sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2}$

Now we substitute these simplified radicals back into the original expression:

$5\sqrt{8} + \sqrt{50} = 5(2\sqrt{2}) + 5\sqrt{2}$

$= 10\sqrt{2} + 5\sqrt{2}$

Since the terms have the same radical $\sqrt{2}$, we can combine them:

$10\sqrt{2} + 5\sqrt{2} = (10+5)\sqrt{2} = 15\sqrt{2}$

3. Final Answer

$15\sqrt{2}$