Question
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Answer
The simplified result is \( -6\sqrt{3} \).
Solution
We start with the expression:
-2√12 - √12
Step 1: Combine the like terms (the radical part √12 is common):
-2√12 - 1√12 = -(2 + 1)√12 = -3√12
Step 2: Simplify √12:
√12 = √(4 × 3) = √4 · √3 = 2√3
Step 3: Substitute back:
-3√12 = -3(2√3) = -6√3
Thus, the simplified result is:
-6√3
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Simplify this solution Beyond the Answer
To simplify \( -2 \sqrt{12} - \sqrt{12} \), first, note that both terms contain the same radical, \( \sqrt{12} \). You can combine them as follows: \[ -2\sqrt{12} - 1\sqrt{12} = (-2 - 1)\sqrt{12} = -3\sqrt{12}. \] Next, simplify \( \sqrt{12} \). Since \( 12 = 4 \times 3 \), we have \( \sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3} \). Substituting this back into the expression gives: \[ -3\sqrt{12} = -3(2\sqrt{3}) = -6\sqrt{3}. \] So, the final simplified form is \( -6\sqrt{3} \).
