To find the roots of the function \( f(x) = x^2 - 48 \), we set \( f(x) \) equal to zero:
\[ x^2 - 48 = 0 \]
Next, we solve for \( x^2 \):
\[ x^2 = 48 \]
Taking the square root of both sides gives:
\[ x = \pm \sqrt{48} \]
We can simplify \( \sqrt{48} \):
\[ \sqrt{48} = \sqrt{16 \cdot 3} = \sqrt{16} \cdot \sqrt{3} = 4\sqrt{3} \]
Thus, the roots are:
\[ x = 4\sqrt{3} \quad \text{and} \quad x = -4\sqrt{3} \]
Therefore, the roots of the function \( f(x) = x^2 - 48 \) are \( -4\sqrt{3} \) and \( 4\sqrt{3} \).
Among the given options, the correct answer is:
Negative 4 StartRoot 3 EndRoot and 4 StartRoot 3 EndRoot.