Questions: Evaluate the radical expression. Express your answer as an integer, simplified fraction, or a decimal rounded to two decimal places. If the expression does not represent a real number, indicate "Not a Real Number". √(-361)

$Evaluate the radical expression. Express your answer as an integer, simplified fraction, or a decimal rounded to two decimal places. If the expression does not represent a real number, indicate "Not a Real Number". √(-361)$

Transcript text: Evaluate the radical expression. Express your answer as an integer, simplified fraction, or a decimal rounded to two decimal places. If the expression does not represent a real number, indicate "Not a Real Number". \[ \sqrt{-361} \]

Solution

Solution Steps

Hint

To solve the square root of a negative number, recognize that it involves imaginary numbers. The square root of a negative number $ -x $ is $ i\sqrt{x} $, where $ i $ is the imaginary unit.

Step 1: Identify the Expression

We are given the expression $ \sqrt{-361} $.

Step 2: Recognize the Nature of the Expression

Since the expression involves the square root of a negative number, it will result in an imaginary number. The square root of a negative number $ -x $ is $ i\sqrt{x} $, where $ i $ is the imaginary unit.

Step 3: Calculate the Square Root

We need to find the square root of the positive part of the expression: \[ \sqrt{361} = 19 \]

Step 4: Apply the Imaginary Unit

Since the original expression was negative, we apply the imaginary unit $ i $: \[ \sqrt{-361} = 19i \]