Question

multiply.
\\(\sqrt{3}(\sqrt{7} + 6)\\)
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\), where \(a = \sqrt{3}\), \(b=\sqrt{7}\) and \(c = 6\). So we have \(\sqrt{3}\times\sqrt{7}+\sqrt{3}\times6\).

Step2: Simplify each term

For the first term, using the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\), we get \(\sqrt{3\times7}= \sqrt{21}\). The second term is \(6\sqrt{3}\). So the expression becomes \(\sqrt{21}+6\sqrt{3}\).

Answer:

\(\sqrt{21}+6\sqrt{3}\)