Question
Subtract. Write your answer in simplest form. \( -9 \sqrt{8}-8 \sqrt{2} \)
Ask by Stanley Franklin. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-26\sqrt{2}\)
Solution
To simplify the expression \( -9 \sqrt{8} - 8 \sqrt{2} \), follow these steps:
1. **Simplify \(\sqrt{8}\):**
\[
\sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}
\]
2. **Substitute \(\sqrt{8}\) back into the original expression:**
\[
-9 \sqrt{8} - 8 \sqrt{2} = -9 \times 2\sqrt{2} - 8\sqrt{2}
\]
3. **Multiply and combine like terms:**
\[
-18\sqrt{2} - 8\sqrt{2} = (-18 - 8)\sqrt{2} = -26\sqrt{2}
\]
**Final Answer:**
\[
-26\sqrt{2}
\]
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Simplify this solution Beyond the Answer
To simplify the expression \( -9 \sqrt{8} - 8 \sqrt{2} \), we first simplify \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \] Now substitute \( \sqrt{8} \) back into the expression: \[ -9 \sqrt{8} = -9 \cdot 2\sqrt{2} = -18\sqrt{2} \] Now the expression becomes: \[ -18\sqrt{2} - 8\sqrt{2} \] We can combine the like terms: \[ -18\sqrt{2} - 8\sqrt{2} = (-18 - 8)\sqrt{2} = -26\sqrt{2} \] Thus, the answer in simplest form is: \[ \boxed{-26\sqrt{2}} \]
