Question

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

Explanation:

Step1: Apply distributive property

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

Step2: Simplify each term

For the first term, \(\sqrt{5}\times4 = 4\sqrt{5}\). For the second term, using the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\) (\(a\geq0,b\geq0\)), we get \(\sqrt{5}\times\sqrt{3}=\sqrt{5\times3}=\sqrt{15}\).

Step3: Combine the terms

Combining the two simplified terms, we have \(4\sqrt{5}+\sqrt{15}\).

Answer:

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