-4 squareroot 6 minus 8 squareroot 96, subract in simplist form

Answer 1

To simplify the expression \(-4\sqrt{6} - 8\sqrt{96}\), we'll first simplify \(\sqrt{96}\).

1. Simplifying \(\sqrt{96}\): \[ \sqrt{96} = \sqrt{16 \cdot 6} = \sqrt{16} \cdot \sqrt{6} = 4\sqrt{6} \]

2. Substituting back into the expression: Now, substitute \(\sqrt{96}\) with \(4\sqrt{6}\) in the expression: \[ -4\sqrt{6} - 8\sqrt{96} = -4\sqrt{6} - 8(4\sqrt{6}) \] \[ = -4\sqrt{6} - 32\sqrt{6} \]

3. Combining like terms: \[ -4\sqrt{6} - 32\sqrt{6} = (-4 - 32)\sqrt{6} = -36\sqrt{6} \]

Thus, the simplified form of the expression \(-4\sqrt{6} - 8\sqrt{96}\) is: \[ \boxed{-36\sqrt{6}} \]