Math Problem Statement
Solution
To evaluate , we need to work with complex numbers since the square root of a negative number is not defined within the set of real numbers.
Step-by-Step Solution:
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Factor out the negative sign:
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Separate the square roots:
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Simplify as , the imaginary unit:
So, the expression becomes:
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Simplify :
- Factor 72 into its prime factors: .
- Use the property of square roots: .
Thus:
Then:
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Combine the results:
Final Answer:
Would you like more details or have any questions about this solution?
Here are 5 related questions to explore further:
- What is the square root of a negative number, such as ?
- How do you simplify square roots of non-perfect squares like ?
- What are imaginary numbers, and why are they important in mathematics?
- Can you explain how to multiply and divide complex numbers?
- How do you represent complex numbers in polar form?
Tip: When dealing with square roots of negative numbers, always factor out first and use the imaginary unit .
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Math Problem Analysis
Mathematical Concepts
Complex Numbers
Square Roots
Imaginary Unit
Formulas
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Theorems
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Suitable Grade Level
Grades 10-12