The given expression is:

$9\sqrt{72} + 2\sqrt{32}$

Step 1: Simplify the Square Roots

Simplifying $\sqrt{72}$:

$\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$

So,

$9\sqrt{72} = 9 \times 6\sqrt{2} = 54\sqrt{2}$

Simplifying $\sqrt{32}$:

$\sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2}$

So,

$2\sqrt{32} = 2 \times 4\sqrt{2} = 8\sqrt{2}$

Step 2: Add Like Terms

Since both terms have $\sqrt{2}$, we can factor:

$54\sqrt{2} + 8\sqrt{2} = (54 + 8)\sqrt{2} = 62\sqrt{2}$

Final Answer:

$\mathbf{62\sqrt{2}}$

Would you like a more detailed breakdown of any step?

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Related Questions:

1. How do you simplify square roots in algebraic expressions?
2. What are the properties of square roots that help in simplification?
3. Can you solve $5\sqrt{50} - 3\sqrt{8}$?
4. How do you factor out common terms in radical expressions?
5. What is the difference between like and unlike radical terms?

Tip:

Always factor numbers inside square roots into perfect squares for easier simplification!