To rewrite \( \sqrt{48} \) as the product of an integer and another irrational square root, we can simplify it as follows:
- First, factor \( 48 \) into \( 16 \times 3 \), since \( 16 \) is a perfect square.
- Then, we take the square root: \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3}. \]
So, the correct answer is \( 4\sqrt{3} \).