Question

multiply. write your answer in simplest form. \\(sqrt{3}(2 + sqrt{2})\\)

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\), where \(a = \sqrt{3}\), \(b = 2\), and \(c=\sqrt{2}\). So we have \(\sqrt{3}\times2+\sqrt{3}\times\sqrt{2}\).

Step2: Simplify each term

For the first term, \(\sqrt{3}\times2 = 2\sqrt{3}\). For the second term, using the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{3}\times\sqrt{2}=\sqrt{3\times2}=\sqrt{6}\).

Answer:

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