Question

simplify to standard form
$-sqrt{-25} = $
$\circ$ $5i$
$\circ$ $-25i$
$\circ$ $25i$
$\bullet$ $-5i$

Explanation:

Step1: Recall the imaginary unit

The imaginary unit \( i \) is defined as \( i = \sqrt{-1} \). So, we can rewrite \( \sqrt{-25} \) as \( \sqrt{25 \times (-1)} \).

Step2: Use the property of square roots

Using the property \( \sqrt{ab} = \sqrt{a} \times \sqrt{b} \) (for \( a\geq0, b\geq0 \), and extended to complex numbers here), we have \( \sqrt{25 \times (-1)}=\sqrt{25}\times\sqrt{-1} \).

Step3: Simplify the square roots

We know that \( \sqrt{25} = 5 \) and \( \sqrt{-1}=i \), so \( \sqrt{-25}=5i \). Then, we have the original expression \( -\sqrt{-25} \), which is \( - (5i)=-5i \).

Answer:

-5i (corresponding to the option with the blue dot, which is the correct one as shown in the calculation)