To simplify the expression [tex]\( 4 \sqrt{72} \)[/tex], we need to break it down step-by-step.
1. Simplify [tex]\( \sqrt{72} \)[/tex]:
- First, we factor 72 to its prime factors: [tex]\( 72 = 36 \times 2 \)[/tex].
- We can then write: [tex]\( \sqrt{72} = \sqrt{36 \times 2} \)[/tex].
- Using the property of square roots, [tex]\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)[/tex], we get: [tex]\( \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} \)[/tex].
- Since [tex]\( \sqrt{36} = 6 \)[/tex], it simplifies further to: [tex]\( 6 \sqrt{2} \)[/tex].
2. Substitute the simplified form of [tex]\( \sqrt{72} \)[/tex] back into the original expression:
- The expression [tex]\( 4 \sqrt{72} \)[/tex] now becomes: [tex]\( 4 \times 6 \sqrt{2} \)[/tex].
- Multiply the constants: [tex]\( 4 \times 6 = 24 \)[/tex].
3. Final simplified form:
- Combine the results: [tex]\( 4 \sqrt{72} = 24 \sqrt{2} \)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{24 \sqrt{2}} \][/tex]
So the correct answer is [tex]\( \text{D. } 24 \sqrt{2} \)[/tex].
