Given:
Consider the complete question is "Which expression is equivalent to [tex]8\sqrt{6}[/tex]? A. [tex]\sqrt{14}[/tex] B. [tex]\sqrt{748}[/tex] C. [tex]\sqrt{196}[/tex] D. [tex]\sqrt{384}[/tex]".
To find:
The equivalent expression.
Solution:
We have,
[tex]8\sqrt{6}[/tex]
It can be written as
[tex]=(\sqrt{8})^2\sqrt{6}[/tex]
[tex]=\sqrt{8}\cdot \sqrt{8}\codt \sqrt{6}[/tex]
[tex]=\sqrt{8\cdot 8\cdot 6}[/tex] [tex][\because \sqrt{a}\sqrt{b}=\sqrt{ab}][/tex]
[tex]=\sqrt{384}[/tex]
So, [tex]\sqrt{384}[/tex] is equivalent to [tex]8\sqrt{6}[/tex].
Therefore, the correct option is D.
