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.

Learn how to simplify 5√72 by breaking down 72 into its prime factors and applying the product property of square roots. This step-by-step solution shows how to reduce the expression to 30√2, perfect for students in Grades 7-9.

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