To rewrite the irrational square root \(\sqrt{48}\) as the product of an integer and another irrational square root, we can first factor 48.
48 can be factored as: \[ 48 = 16 \times 3 \] We know that \(\sqrt{16} = 4\), so we can rewrite \(\sqrt{48}\) as: \[ \sqrt{48} = \sqrt{16 \times 3} = \sqrt{16} \times \sqrt{3} = 4\sqrt{3} \]
So, \(\sqrt{48}\) can be written as \(4\sqrt{3}\).
Thus, the correct response from the options given would be: \[ 4\sqrt{12} \] This is not directly accurate because we did not factor out a perfect square. Hence, the correct response you are looking for based on your format would be: \[ 4\sqrt{3} \]
Please note that from the options you've provided, none directly represent \(\sqrt{48}\) rewritten correctly. But the intention of rewriting \(\sqrt{48}\) based on direct factorization yields \(4\sqrt{3}\). If "4 start root 12 end root" was meant to represent something close, the accurate form from standard calculations should be \(4\sqrt{3}\).