https://file.aiquickdraw.com/mathbot/file/17301245732395fp4h2xw.jpg

To solve the given problem, we need to evaluate the expression \(18 - \sqrt{-25}\).

### Step 1: Evaluate the square root of \(-25\)
The square root of a negative number involves imaginary numbers. Specifically, \(\sqrt{-25}\) can be rewritten as:
\[
\sqrt{-25} = \sqrt{25} \cdot \sqrt{-1} = 5i
\]
where \(i\) is the imaginary unit (\(i = \sqrt{-1}\)).

### Step 2: Substitute back into the expression
Now, replace \(\sqrt{-25}\) with \(5i\):
\[
18 - \sqrt{-25} = 18 - 5i
\]

### Step 3: Select the correct option
The equivalent expression is \(18 - 5i\). Thus, the correct answer is:
**18 - 5i**

Would you like further explanation or details on this problem? Here are some related questions to consider:

1. How do you calculate the square root of other negative numbers?
2. What is the definition of an imaginary number?
3. How do imaginary numbers interact with real numbers in addition and subtraction?
4. What are the properties of the imaginary unit \(i\)?
5. How would this problem change if \(\sqrt{-25}\) were replaced with \(\sqrt{-36}\)?

**Tip:** When dealing with square roots of negative numbers, always remember that the result involves \(i\), representing the square root of \(-1\).

Which of the following is equivalent to 18 - √(-25)?

Learn how to evaluate the complex expression 18 - √(-25) by understanding imaginary numbers and using the imaginary unit i. This solution is designed for students in Grades 10-12, covering the concepts of complex and imaginary numbers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation