Question

4 radical3 + 2 radical48 in simplest form

Answer 1

To simplify the expression \(4\sqrt{3} + 2\sqrt{48}\), we first simplify the term \(2\sqrt{48}\):

1. Factor \(48\):
\[
48 = 16 \times 3 = 4^2 \times 3
\]

2. Simplify \(\sqrt{48}\):
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]

3. Now substitute back into the expression:
\[
2\sqrt{48} = 2 \times 4\sqrt{3} = 8\sqrt{3}
\]

4. Combine like terms:
\[
4\sqrt{3} + 8\sqrt{3} = (4 + 8)\sqrt{3} = 12\sqrt{3}
\]

Thus, the expression \(4\sqrt{3} + 2\sqrt{48}\) simplifies to \(\boxed{12\sqrt{3}}\).