Question
Subtract. Write your answer in simplest form. \( -10 \sqrt{22}-\sqrt{88} \)
Ask by Chang Dickson. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-12\sqrt{22}\)
Solution
To simplify the expression \( -10 \sqrt{22} - \sqrt{88} \), follow these steps:
1. **Simplify \(\sqrt{88}\):**
\[
\sqrt{88} = \sqrt{4 \times 22} = \sqrt{4} \times \sqrt{22} = 2\sqrt{22}
\]
2. **Substitute back into the original expression:**
\[
-10\sqrt{22} - \sqrt{88} = -10\sqrt{22} - 2\sqrt{22}
\]
3. **Combine like terms:**
\[
(-10 - 2)\sqrt{22} = -12\sqrt{22}
\]
**Final Answer:**
\(-12\,\sqrt{22}\)
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Simplify this solution Beyond the Answer
To simplify the expression \( -10 \sqrt{22}-\sqrt{88} \), first, we note that \( \sqrt{88} \) can be simplified. Since \( 88 = 4 \times 22 \), we find that: \[ \sqrt{88} = \sqrt{4 \times 22} = \sqrt{4} \times \sqrt{22} = 2\sqrt{22}. \] Now, we can substitute this back into the expression: \[ -10 \sqrt{22} - \sqrt{88} = -10 \sqrt{22} - 2\sqrt{22}. \] Combining the like terms gives us: \[ -10 \sqrt{22} - 2 \sqrt{22} = (-10 - 2) \sqrt{22} = -12 \sqrt{22}. \] Thus, the answer in simplest form is: \[ \boxed{-12 \sqrt{22}}. \]
