Let's simplify the expression [tex]\(4 \sqrt{72}\)[/tex] step-by-step.
1. Simplify the expression inside the square root:
[tex]\[
\sqrt{72}
\][/tex]
Notice that [tex]\(72\)[/tex] can be factored into [tex]\(72 = 36 \times 2\)[/tex]. We can then use the property of square roots that states [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex] to simplify:
[tex]\[
\sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2}
\][/tex]
2. Simplify the square root of [tex]\(36\)[/tex]:
[tex]\[
\sqrt{36} = 6
\][/tex]
Then, substitute back into the expression:
[tex]\[
\sqrt{72} = 6 \sqrt{2}
\][/tex]
3. Multiply this result by 4:
[tex]\[
4 \sqrt{72} = 4 \times (6 \sqrt{2}) = 4 \times 6 \times \sqrt{2} = 24 \sqrt{2}
\][/tex]
Thus, the simplified form of [tex]\(4 \sqrt{72}\)[/tex] is [tex]\(24 \sqrt{2}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{24 \sqrt{2}}
\][/tex]
