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Answer
The simplified form is \( -10\sqrt{3} \).
Solution
Given the expression \( -5\sqrt{12} \), we begin by simplifying the radical \( \sqrt{12} \).
1. Factor \( 12 \) as \( 4 \times 3 \):
\[
\sqrt{12} = \sqrt{4 \times 3}
\]
2. Use the property of radicals:
\[
\sqrt{12} = \sqrt{4} \cdot \sqrt{3}
\]
3. Simplify \( \sqrt{4} \):
\[
\sqrt{4} = 2
\]
So,
\[
\sqrt{12} = 2\sqrt{3}
\]
4. Substitute back into the original expression:
\[
-5\sqrt{12} = -5(2\sqrt{3}) = -10\sqrt{3}
\]
The simplified form is: \( -10\sqrt{3} \).
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Simplify this solution Bonus Knowledge
To simplify \( -5 \sqrt{12} \), we start by breaking down the square root of 12. Since \( 12 = 4 \times 3 \), we can write: \[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \cdot \sqrt{3} = 2\sqrt{3} \] Now substituting this back into the expression gives us: \[ -5 \sqrt{12} = -5 (2\sqrt{3}) = -10\sqrt{3} \] So, the simplified form of \( -5 \sqrt{12} \) is \( -10\sqrt{3} \).
