Question

simplify $sqrt{5}(6 - 4sqrt{3})$. a. 9 b. $30sqrt{3}$ c. $6sqrt{5}-4sqrt{15}$ d. $sqrt{30}-20sqrt{3}$

Explanation:

Step1: Use distributive property

\[

$$\begin{align*} \sqrt{5}(6 - 4\sqrt{3})&=\sqrt{5}\times6-\sqrt{5}\times4\sqrt{3}\\ & = 6\sqrt{5}-4\sqrt{5\times3}\\ \end{align*}$$

\]

Step2: Simplify the square - root product

Since \(5\times3 = 15\), we have \(6\sqrt{5}-4\sqrt{15}\)

Answer:

\(6\sqrt{5}-4\sqrt{15}\)