Question

Combine the radicals using addition and subtraction, if possible.

5√48 −6√3 +2√12


(1 point)

Answer 1

To combine the radicals \(5\sqrt{48} - 6\sqrt{3} + 2\sqrt{12}\), we first simplify each radical term.

1. **Simplify \( \sqrt{48} \)**:
\[
\sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}
\]
So,
\[
5\sqrt{48} = 5 \times 4\sqrt{3} = 20\sqrt{3}
\]

2. **Simplify \( \sqrt{12} \)**:
\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}
\]
So,
\[
2\sqrt{12} = 2 \times 2\sqrt{3} = 4\sqrt{3}
\]

Now we can rewrite the expression with the simplified radicals:
\[
20\sqrt{3} - 6\sqrt{3} + 4\sqrt{3}
\]

Next, we combine the like terms (the coefficients of \(\sqrt{3}\)):
\[
(20 - 6 + 4)\sqrt{3} = 18\sqrt{3}
\]

Therefore, the combined expression is:
\[
\boxed{18\sqrt{3}}
\]