https://file.aiquickdraw.com/mathbot/file/172987866941519taybe4.jpg

Let's simplify the given expression:

We are tasked with simplifying \( 4 \sqrt{147} \).

1. First, factorize 147:  
   \[
   147 = 3 \times 49 = 3 \times 7^2
   \]

2. Using this factorization, we can rewrite \( \sqrt{147} \):
   \[
   \sqrt{147} = \sqrt{3 \times 7^2} = 7\sqrt{3}
   \]

3. Now, multiply by 4:
   \[
   4 \sqrt{147} = 4 \times 7\sqrt{3} = 28\sqrt{3}
   \]

Thus, the simplified expression is \( 28\sqrt{3} \), which corresponds to option D.

Would you like more details or have any questions?

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Here are 5 related questions to deepen your understanding:
1. How do you factorize square roots more efficiently?
2. Can you explain why \( \sqrt{7^2} \) simplifies to just 7?
3. How would you simplify \( 6 \sqrt{75} \)?
4. Why do we multiply outside terms and leave square roots intact?
5. What happens if the number inside the square root is already prime?

**Tip**: When simplifying square roots, always look for perfect squares inside the radical.

Cedric wrote the following expression on the board: 4√147. Which expression is equivalent to the one he wrote? A) 196√3 B) 12√7 C) 3√7 D) 28√3

Learn how to simplify the radical expression 4√147 by using factorization and multiplication of square roots. This problem helps students in Grades 8-10 practice simplifying complex square root expressions. The solution involves breaking down the number 147 into prime factors and simplifying step by step.

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