Question

1. $3sqrt{12} + 2sqrt{8} - sqrt{2}$

Explanation:

Step1: Simplify each radical

Simplify \(3\sqrt{12}\): \(12 = 4\times3\), so \(\sqrt{12}=\sqrt{4\times3}=2\sqrt{3}\), then \(3\sqrt{12}=3\times2\sqrt{3}=6\sqrt{3}\).

Simplify \(2\sqrt{8}\): \(8 = 4\times2\), so \(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\), then \(2\sqrt{8}=2\times2\sqrt{2}=4\sqrt{2}\).

Step2: Combine like terms

Now the expression becomes \(6\sqrt{3}+4\sqrt{2}-\sqrt{2}\). Combine the \(\sqrt{2}\) terms: \(4\sqrt{2}-\sqrt{2}=(4 - 1)\sqrt{2}=3\sqrt{2}\).

So the simplified expression is \(6\sqrt{3}+3\sqrt{2}\).

Answer:

\(6\sqrt{3}+3\sqrt{2}\)