squareroot3(-9-squareroot2)

1 answer

To simplify the expression \( \sqrt{3}(-9 - \sqrt{2}) \), follow these steps:

  1. Distribute \( \sqrt{3} \) to both terms inside the parentheses: \[ \sqrt{3} \cdot (-9) + \sqrt{3} \cdot (-\sqrt{2}) \]

  2. Perform the multiplication:

    • For the first term: \[ -9\sqrt{3} \]
    • For the second term: \[ -\sqrt{3} \cdot \sqrt{2} = -\sqrt{6} \]
  3. Combine the terms: \[ -9\sqrt{3} - \sqrt{6} \]

Thus, the simplified expression is: \[ -9\sqrt{3} - \sqrt{6} \]