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Use the product rule to simplify the radical. \[ 8 \sqrt{4} \]

Ask by Moreno Craig. in the United States
Jan 22,2025

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The simplified form of \( 8 \sqrt{4} \) is \( 16 \).

Solución

To simplify the expression \( 8 \sqrt{4} \) using the product rule for radicals, follow these steps: ### Step 1: Understand the Components - **8** is a constant outside the radical. - **\(\sqrt{4}\)** is the square root of 4. ### Step 2: Simplify the Radical First, simplify \(\sqrt{4}\): \[ \sqrt{4} = 2 \] ### Step 3: Multiply the Constants Now, multiply the simplified radical by 8: \[ 8 \times 2 = 16 \] ### Conclusion So, the simplified form of \( 8 \sqrt{4} \) is: \[ 16 \] **Answer:** \( 16 \)

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Bonus Knowledge

To simplify \( 8 \sqrt{4} \), we start by calculating \( \sqrt{4} \), which equals 2. Then, we multiply: \[ 8 \sqrt{4} = 8 \times 2 = 16. \] So, the simplified result is 16! Radicals can be a lot of fun, especially when you realize how they can transform simple numbers into something more substantial. Remember, whenever you encounter a radical, it's often beneficial to first evaluate the square root before performing any multiplications. This way, you can make calculations smoother and your final answer clearer!

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