Answer:
[tex]$ \mbox{\Large $ 108$ } $\\[/tex]
Step-by-step explanation:
1.) Expand the radicand, the expression that is under a radical sign.
⇒ [tex]4\sqrt{3^6} = 4 \cdot \sqrt{3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3} = 4 \cdot \sqrt{3 \cdot 3} \cdot \sqrt{3 \cdot 3} \cdot \sqrt{3 \cdot 3} = 4 \cdot \sqrt{3^2} \cdot \sqrt{3^2} \cdot \sqrt{3^2}[/tex]
2.) Get the square root of the radicands that are perfect squares and simplify. In this case, it is the [tex]$ \mbox{\Large $ 3^2$ } $[/tex].
⇒ [tex]4 \cdot \sqrt{3^2} \cdot \sqrt{3^2} \cdot \sqrt{3^2} = 4 \cdot 3 \cdot 3 \cdot 3 = 12 \cdot 3 \cdot 3 = 36 \cdot 3 = \bold{108}[/tex]
3.) Therefore, the simplified form of the expression [tex]4\sqrt{3^6}[/tex] is [tex]108[/tex].
I hope this helps you understand this concept in Mathematics.
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