Questions: Write the number in simplest form, without a negative radicand. √(-169) A. ± 13 B. -i √13 C. 13 i D. -13 i

Solution Steps

To simplify the expression \(\sqrt{-169}\), recognize that the square root of a negative number involves the imaginary unit \(i\), where \(i = \sqrt{-1}\). Thus, \(\sqrt{-169} = \sqrt{169} \cdot \sqrt{-1} = 13i\).

We start with the expression \( \sqrt{-169} \). Since the radicand is negative, we will use the imaginary unit \( i \), where \( i = \sqrt{-1} \).

We can rewrite the expression as: \[ \sqrt{-169} = \sqrt{169} \cdot \sqrt{-1} \] Calculating each part, we find: \[ \sqrt{169} = 13 \quad \text{and} \quad \sqrt{-1} = i \] Thus, we have: \[ \sqrt{-169} = 13i \]

The simplified form of \( \sqrt{-169} \) is \( 13i \).

Final Answer