To simplify the expression [tex]\( 4 \sqrt{72} \)[/tex], follow these steps:
1. Factorize the number under the square root:
[tex]\[
72 = 36 \times 2
\][/tex]
2. Rewrite the square root using the factorized form:
[tex]\[
\sqrt{72} = \sqrt{36 \times 2}
\][/tex]
3. Use the property of square roots to separate the factors:
[tex]\[
\sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2}
\][/tex]
4. Simplify the square root of 36:
[tex]\[
\sqrt{36} = 6
\][/tex]
Hence,
[tex]\[
\sqrt{36 \times 2} = 6 \times \sqrt{2}
\][/tex]
5. Multiply the result by 4:
[tex]\[
4 \times \sqrt{72} = 4 \times (6 \times \sqrt{2}) = 4 \times 6 \times \sqrt{2} = 24 \sqrt{2}
\][/tex]
Thus, the simplified form of [tex]\( 4 \sqrt{72} \)[/tex] is [tex]\( 24 \sqrt{2} \)[/tex].
Therefore, the correct answer is:
D. [tex]\( 24 \sqrt{2} \)[/tex]
