Question
Simplify the expression \[ 14 \sqrt{5}+4 \sqrt{20} \] ?
Ask by Romero Schultz. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The simplified expression is \( 22 \sqrt{5} \).
Solution
To simplify the expression:
\[
14 \sqrt{5} + 4 \sqrt{20}
\]
follow these steps:
1. **Simplify \(\sqrt{20}\):**
\[
\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2 \sqrt{5}
\]
2. **Substitute back into the original expression:**
\[
14 \sqrt{5} + 4 \times 2 \sqrt{5} = 14 \sqrt{5} + 8 \sqrt{5}
\]
3. **Combine like terms:**
\[
14 \sqrt{5} + 8 \sqrt{5} = (14 + 8) \sqrt{5} = 22 \sqrt{5}
\]
**Final Answer:**
\[
22 \sqrt{5}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To simplify the expression \( 14 \sqrt{5}+4 \sqrt{20} \), we first need to simplify \( \sqrt{20} \). We know that: \[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \cdot \sqrt{5} = 2 \sqrt{5}. \] Now we can substitute \( \sqrt{20} \) back into the expression: \[ 4 \sqrt{20} = 4 \cdot 2 \sqrt{5} = 8 \sqrt{5}. \] Now, we can combine the like terms: \[ 14 \sqrt{5} + 8 \sqrt{5} = (14 + 8) \sqrt{5} = 22 \sqrt{5}. \] Therefore, the simplified expression is: \[ \boxed{22 \sqrt{5}}. \]
