Question
Subtract. Write your answer in simplest form. \( -2 \sqrt{75}-6 \sqrt{3} \)
Ask by Salinas Salazar. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\(-16\sqrt{3}\)
Solution
To simplify the expression \(-2\sqrt{75} - 6\sqrt{3}\), follow these steps:
1. **Simplify \(\sqrt{75}\):**
\[
\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}
\]
2. **Substitute back into the original expression:**
\[
-2\sqrt{75} - 6\sqrt{3} = -2(5\sqrt{3}) - 6\sqrt{3}
\]
3. **Multiply the constants:**
\[
-10\sqrt{3} - 6\sqrt{3} = (-10 - 6)\sqrt{3} = -16\sqrt{3}
\]
So, the expression in its simplest form is:
\(-16\sqrt{3}\)
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To simplify \( -2 \sqrt{75} - 6 \sqrt{3} \), first simplify \( \sqrt{75} \). We can express \( \sqrt{75} \) as \( \sqrt{25 \times 3} = 5 \sqrt{3} \). Now substitute back into the expression: \( -2 \cdot 5 \sqrt{3} - 6 \sqrt{3} \). This becomes: \( -10 \sqrt{3} - 6 \sqrt{3} = -16 \sqrt{3} \). Thus, the answer is \( -16 \sqrt{3} \).
