For this case we must simplify the following expression:
[tex]4 \sqrt {\frac {3} {2} x}[/tex]
We have to define properties of powers and roots that:
[tex]\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}\\a \sqrt [n] {b} = \sqrt [n] {a ^ n * b}[/tex]
Then, rewriting the expression we have:
[tex]\sqrt {4 ^ 2 * \frac {3} {2} x} =\\\sqrt {16 * \frac {3} {2} x} =\\\sqrt {\frac {48} {2} x} =\\\sqrt {24x} =\\\sqrt {2 ^ 2 * 6 * x} =\\2 \sqrt {6x}[/tex]
Answer
[tex]2\sqrt{6x}[/tex]
