Question

simplify.\
\\(\sqrt{2}\left(\sqrt{8} + \sqrt{6}\
ight)\\)

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\), where \(a = \sqrt{2}\), \(b=\sqrt{8}\), and \(c = \sqrt{6}\). So we get \(\sqrt{2}\times\sqrt{8}+\sqrt{2}\times\sqrt{6}\).

Step2: Use property of square roots \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\)

For the first term: \(\sqrt{2}\times\sqrt{8}=\sqrt{2\times8}=\sqrt{16}\). For the second term: \(\sqrt{2}\times\sqrt{6}=\sqrt{2\times6}=\sqrt{12}\).

Step3: Simplify square roots

Simplify \(\sqrt{16}\) and \(\sqrt{12}\). We know that \(\sqrt{16} = 4\) and \(\sqrt{12}=\sqrt{4\times3}=\sqrt{4}\times\sqrt{3}=2\sqrt{3}\).

Step4: Combine results

Combining the simplified terms, we have \(4 + 2\sqrt{3}\).

Answer:

\(4 + 2\sqrt{3}\)