Question

Which choices are equivalent to the expression below? Check all that appl6√3

Answer 1

Given:

$6\sqrt{3}$

And we know that:

$6\sqrt{3}=\sqrt{36\times3}=\sqrt{108}$

Check each of the options:

$\begin{gathered} A.\sqrt{18}\cdot\sqrt{6}=\sqrt{18\cdot6}=\sqrt{108} \\ so,\text{ A is equivalent to 6}\sqrt{3} \end{gathered}$$B.\sqrt{54}\text{ is not equivalent to 6}\sqrt{3}$$C.\text{ }108\text{ is not equivalent to 6}\sqrt{3}$$\begin{gathered} D.\sqrt{3}\cdot\sqrt{36}=\sqrt{3\cdot36}=\sqrt{108} \\ so,\text{ D is equivalent to 6}\sqrt{3} \end{gathered}$$\begin{gathered} E.\sqrt{108} \\ so,\text{ E is equivalent to 6}\sqrt{3} \end{gathered}$$\begin{gathered} F.\sqrt{3}\sqrt{6}=\sqrt{3\cdot6}=\sqrt{18} \\ so,\text{ F is not equivalent to 6}\sqrt{3} \end{gathered}$

Answer:

A, D and E