Math Problem Statement
Solution
To solve this problem, we need to simplify the expression and match it to one of the given answer choices.
Step 1: Simplify the Square Root of a Negative Number
The expression inside the square root is . Since this is a negative number, we can rewrite it using , where :
Step 2: Simplify
We can simplify by factoring out a perfect square:
Therefore,
Step 3: Multiply by 2
Now, substitute back into the original expression:
Answer
The correct answer is:
Would you like further details or have any questions?
Here are five related questions for further practice:
- What is the value of in terms of ?
- How would you simplify ?
- What is the principal square root of ?
- How do you simplify ?
- How does affect the simplification of square roots of negative numbers?
Tip: Remember that , which is useful for handling square roots of negative numbers in complex numbers.
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Square Roots
Imaginary Numbers
Formulas
√(-a) = i√(a), where i = √(-1)
Simplification of square roots of negative numbers
Theorems
Properties of Imaginary Numbers
Suitable Grade Level
Grades 10-12