Question

-2 squareroot 48 + 4 squareroot 3

Answer 1

To simplify the expression \(-2 \sqrt{48} + 4 \sqrt{3}\), we start by simplifying \(\sqrt{48}\).

1. First, factor \(48\):
\[
48 = 16 \times 3
\]
Thus, we can write:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]

2. Substitute \(\sqrt{48}\) in the expression:
\[
-2 \sqrt{48} + 4 \sqrt{3} = -2(4\sqrt{3}) + 4\sqrt{3}
\]

3. Simplify further:
\[
-2(4\sqrt{3}) = -8\sqrt{3}
\]
Therefore, the expression becomes:
\[
-8\sqrt{3} + 4\sqrt{3}
\]

4. Combine like terms:
\[
-8\sqrt{3} + 4\sqrt{3} = (-8 + 4)\sqrt{3} = -4\sqrt{3}
\]

So, the final simplified result is:
\[
\boxed{-4\sqrt{3}}
\]