Simplify

Problem

√(,−12−(√(,−11)−√(,5)))

Solution

1. Express the square roots of negative numbers using the imaginary unit i where √(,−1)=i

√(,−12)=√(,12)*i=2√(,3)*i

√(,−11)=√(,11)*i

2. Substitute these values back into the original expression.

√(,2√(,3)*i−(√(,11)*i−√(,5)))

3. Distribute the negative sign inside the radicand.

√(,2√(,3)*i−√(,11)*i+√(,5))

4. Group the real and imaginary parts within the square root.

√(,√(,5)+(2√(,3)−√(,11))*i)

Final Answer

√(,−12−(√(,−11)−√(,5)))=√(,√(,5)+(2√(,3)−√(,11))*i)

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