Answer: Third Choice. 3i√3
Step-by-step explanation:
Concept:
Here, we need to know the idea of radical expression and an imaginary number.
A radical expression is any mathematical expression containing a radical symbol. If you need to multiply the number outside of radical back into the radical, then you need to square the number then multiply.
- For example: 2√5. We need to first square 2, which gives us 4. Then, it becomes √(4 × 5) = √20
Imaginary numbers are the numbers when squared it gives the negative result. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.
Solve:
3√3 = √(3 × 3²) = √27 FALSE
-3√(3i) = √(3i × (-3)²) = √27i FALSE
3i√3 = √(3 × (3i)²) = √-27 TRUE
3√(3i) = √(3i × 3²) = √27i FALSE
As we can see from above, only the third choice equals √-27.
Hope this helps!! :)
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