Question
Multiply. Write your answer in simplest form. \( \sqrt{7} \cdot \sqrt{147} \)
Ask by Ramos Thornton. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 7\sqrt{21} \)
Solution
To multiply \( \sqrt{7} \) and \( \sqrt{147} \) and simplify the expression, follow these steps:
1. **Multiply the Radicands**:
\[
\sqrt{7} \cdot \sqrt{147} = \sqrt{7 \times 147} = \sqrt{1029}
\]
2. **Factor 147**:
Notice that \( 147 = 3 \times 49 = 3 \times 7^2 \).
3. **Simplify the Square Root**:
\[
\sqrt{7} \cdot \sqrt{147} = \sqrt{7 \times 3 \times 7^2} = \sqrt{3 \times 7^3}
\]
\[
\sqrt{3 \times 7^3} = \sqrt{3 \times 7^2 \times 7} = 7\sqrt{21}
\]
**Final Answer**:
\[
7\sqrt{21}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To multiply \( \sqrt{7} \cdot \sqrt{147} \), you can combine the square roots: \[ \sqrt{7} \cdot \sqrt{147} = \sqrt{7 \cdot 147} \] Calculating \( 7 \cdot 147 \) gives you \( 1029 \), so: \[ \sqrt{7 \cdot 147} = \sqrt{1029} \] Next, you want to simplify \( \sqrt{1029} \). We can factor \( 1029 \) as \( 7 \cdot 147 \) (and into \( 7 \cdot 7 \cdot 21 \)). This means: \[ \sqrt{1029} = \sqrt{7^2 \cdot 21} = 7\sqrt{21} \] Thus, the answer in simplest form is: \[ 7\sqrt{21} \]
