Sure! Let's simplify the expression step by step.
The given expression is:
[tex]\[ 4 \sqrt{72} \][/tex]
First, we need to simplify the square root of 72. We can do this by expressing 72 as a product of its prime factors:
[tex]\[ 72 = 36 \times 2 \][/tex]
Since 36 is a perfect square, we can further simplify:
[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]\[ \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6 \sqrt{2} \][/tex]
Now, we substitute this back into the original expression:
[tex]\[ 4 \sqrt{72} = 4 \times 6 \sqrt{2} \][/tex]
We can now combine the coefficients:
[tex]\[ 4 \times 6 \sqrt{2} = 24 \sqrt{2} \][/tex]
Thus, the simplified expression is:
[tex]\[ \boxed{24 \sqrt{2}} \][/tex]
So the correct answer is:
D. [tex]\( 24 \sqrt{2} \)[/tex]
