Which of the following is the correct notation for the complex number \( 93+\sqrt{-75} ? \)

To express the complex number \( 93 + \sqrt{-75} \) in standard form, we first need to simplify \( \sqrt{-75} \). Recall that \( \sqrt{-1} \) is denoted as \( i \), where \( i \) is the imaginary unit. Therefore, we can rewrite \( \sqrt{-75} \) as follows: \[ \sqrt{-75} = \sqrt{75} \cdot \sqrt{-1} = \sqrt{75} \cdot i \] Next, we simplify \( \sqrt{75} \): \[ \sqrt{75} = \sqrt{25 \cdot 3} = \sqrt{25} \cdot \sqrt{3} = 5\sqrt{3} \] Now substituting this back into our expression for \( \sqrt{-75} \): \[ \sqrt{-75} = 5\sqrt{3} \cdot i \] Now we can rewrite the original complex number: \[ 93 + \sqrt{-75} = 93 + 5\sqrt{3} i \] Thus, the correct notation for the complex number \( 93 + \sqrt{-75} \) in standard form \( a + bi \) is: \[ \boxed{93 + 5\sqrt{3} i} \]