Question
Use the product rule to simplify the radical. \( -7 \sqrt{27} \)
Ask by Perkins Harris. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-21\sqrt{3}\)
Solution
To simplify the expression \(-7 \sqrt{27}\) using the product rule, follow these steps:
1. **Factor the Radicand**:
\[
27 = 9 \times 3 = (3^2) \times 3
\]
2. **Apply the Product Rule**:
\[
\sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \times \sqrt{3} = 3\sqrt{3}
\]
3. **Multiply by the Coefficient**:
\[
-7 \times 3\sqrt{3} = -21\sqrt{3}
\]
**Simplified Expression**:
\[
-21\sqrt{3}
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution The Deep Dive
To simplify \( -7 \sqrt{27} \), first, note that 27 can be broken down into \( 9 \times 3 \). So, we can rewrite the square root as \( -7 \sqrt{9 \times 3} \). Using the product rule for radicals, this becomes \( -7 \sqrt{9} \cdot \sqrt{3} \). Since the square root of 9 is 3, we have \( -7 \cdot 3 \cdot \sqrt{3} = -21 \sqrt{3} \). So, the simplified form is \( -21 \sqrt{3} \).
