ANSWER
[tex] 4 \sqrt{3} [/tex]
EXPLANATION
We want to simplify;
[tex] {48}^{ \frac{1}{2} } [/tex]
We rewrite this as
[tex] = \sqrt{48} [/tex]
We try to remove the perfect square to obtain,
[tex] = \sqrt{16 \times 3} [/tex]
Recall that,
[tex] \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} [/tex]
We apply this property to obtain,
[tex] = \sqrt{16} \times \sqrt{3} [/tex]
This simplifies to,
[tex] = 4 \sqrt{3} [/tex]
