To simplify $5\sqrt{72}$:

1. Break down 72 into its prime factors:
   $72 = 2^3 \times 3^2$

2. Now, separate the perfect square factor:
   $\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2}$

3. Multiply this result by 5:
   $5\sqrt{72} = 5 \times 6\sqrt{2} = 30\sqrt{2}$

Thus, the simplified form of $5\sqrt{72}$ is: $30\sqrt{2}$

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How do you simplify $7\sqrt{50}$?
2. What is the simplified form of $8\sqrt{18}$?
3. How do you rationalize the denominator of $\frac{3}{\sqrt{5}}$?
4. Can you simplify $\sqrt{200}$ further?
5. What is $\sqrt{a^2b^3}$ in simplified form?

Tip: When simplifying square roots, always look for perfect square factors to break down the expression further.