Question

multiply.
\sqrt{5}(4 + \sqrt{3})
simplify your answer as much as possible.

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\), here \(a = \sqrt{5}\), \(b = 4\), \(c=\sqrt{3}\). So we have \(\sqrt{5}\times4+\sqrt{5}\times\sqrt{3}\).

Step2: Simplify each term

Simplify \(\sqrt{5}\times4 = 4\sqrt{5}\) and \(\sqrt{5}\times\sqrt{3}=\sqrt{5\times3}=\sqrt{15}\) (using the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\) for \(a\geq0,b\geq0\)).

Answer:

\(4\sqrt{5}+\sqrt{15}\)