Evaluate square root of -28

Problem

√(,−28)

Solution

1. Identify the square root of a negative number by using the imaginary unit i where √(,−1)=i

√(,−28)=√(,28)⋅√(,−1)

√(,−28)=√(,28)*i

2. Factor the radicand 28 into its prime factors to find the largest perfect square.

28=4⋅7

28=2⋅7

3. Simplify the radical by taking the square root of the perfect square factor.

√(,28)=√(,4⋅7)

√(,28)=2√(,7)

4. Combine the simplified radical with the imaginary unit.

√(,−28)=2√(,7)*i

Final Answer

√(,−28)=2*i√(,7)

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