Question
Use the product rule to simplify the radical. \[ 8 \sqrt{4} \]
Ask by Moreno Craig. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified form of \( 8 \sqrt{4} \) is \( 16 \).
Solution
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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Simplify this solution 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!
