Let's simplify the given expression step by step:

$6\sqrt{8} + 5\sqrt{50}$

Step 1: Simplify the Square Roots

We break down the radicals into their simplest form.

• $\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}$
• $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$

Step 2: Substitute Back

$6\sqrt{8} = 6 \times 2\sqrt{2} = 12\sqrt{2}$ $5\sqrt{50} = 5 \times 5\sqrt{2} = 25\sqrt{2}$

Step 3: Combine Like Terms

Since both terms have $\sqrt{2}$, we add the coefficients:

$12\sqrt{2} + 25\sqrt{2} = (12 + 25)\sqrt{2} = 37\sqrt{2}$

Final Answer:

$\mathbf{37\sqrt{2}}$

Would you like a more detailed explanation? Let me know if you have any questions!

Here are 5 related problems to practice:

1. Simplify $4\sqrt{18} + 3\sqrt{8}$.
2. Express $7\sqrt{27} - 2\sqrt{12}$ in simplest radical form.
3. Simplify $5\sqrt{24} + 2\sqrt{54}$.
4. Express $6\sqrt{75} + 4\sqrt{48}$ in simplest radical form.
5. Simplify $9\sqrt{50} - 3\sqrt{8}$.

Tip: Always break down radicals into their prime factors to simplify expressions efficiently.