Questions: Write the expression in terms of i and simplify. √(-225)=

Solution Steps

To solve the given problem, we need to express the square root of a negative number in terms of the imaginary unit \(i\). The imaginary unit \(i\) is defined as \(\sqrt{-1}\). Therefore, we can rewrite \(\sqrt{-225}\) using \(i\).

1. Recognize that \(\sqrt{-225}\) can be expressed as \(\sqrt{225} \times \sqrt{-1}\).
2. Simplify \(\sqrt{225}\) to 15.
3. Combine the results to get \(15i\).

To solve \(\sqrt{-225}\), we need to express it in terms of the imaginary unit \(i\), where \(i = \sqrt{-1}\).

We can rewrite \(\sqrt{-225}\) as: \[ \sqrt{-225} = \sqrt{225 \times -1} = \sqrt{225} \times \sqrt{-1} \]

We know that: \[ \sqrt{225} = 15 \quad \text{and} \quad \sqrt{-1} = i \] Thus: \[ \sqrt{-225} = 15i \]

Final Answer