Question

multiply. write your answer in simplest form. \\(\sqrt{5}\left(6 + \sqrt{3}\
ight)\\)

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\), where \(a = \sqrt{5}\), \(b = 6\) and \(c=\sqrt{3}\). So we have \(\sqrt{5}\times6+\sqrt{5}\times\sqrt{3}\).

Step2: Simplify each term

For the first term, \(\sqrt{5}\times6 = 6\sqrt{5}\). For the second term, using the property \(\sqrt{a}\times\sqrt{b}=\sqrt{ab}\), we get \(\sqrt{5}\times\sqrt{3}=\sqrt{5\times3}=\sqrt{15}\).

Answer:

\(6\sqrt{5}+\sqrt{15}\)