Answer:
[tex]$ \mbox{\Large $ 12\sqrt{2}$ } $\\[/tex]
Step-by-step explanation:
1.) Expand the radicand, the expression that is under a radical sign.
⇒ [tex]3\sqrt{2^5} = 3 \cdot \sqrt{2 \cdot 2 \cdot 2 \cdot 2 \cdot 2} = 3 \cdot \sqrt{2 \cdot 2 \cdot 2 \cdot 2} \cdot \sqrt{2} = 3 \cdot \sqrt{2^4} \cdot \sqrt{2}[/tex]
2.) Get the square root of the radicands that are perfect squares and simplify. In this case, it is the [tex]$ \mbox{\Large $ 2^4$ } $[/tex].
⇒ [tex]3 \cdot \sqrt{2^4} \cdot \sqrt{2} = 3 \cdot \sqrt{(2^2)^2} \cdot \sqrt{2} = 3 \cdot (2^2) \cdot \sqrt{2} = 3 \cdot 4 \cdot \sqrt{2} = 12 \cdot \sqrt{2} = \bold{12\sqrt{2}}[/tex]
3.) Therefore, the simplified form of the expression [tex]3\sqrt{2^5}[/tex] is [tex]12\sqrt{2}[/tex].
I hope this helps you understand this concept in Mathematics.
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