Evaluate square root of -63

Problem

√(,−63)

Solution

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

√(,−63)=√(,63)⋅√(,−1)

√(,−63)=√(,63)*i

2. Factor the radicand to find the largest perfect square factor of 63

63=9⋅7

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

√(,9⋅7)*i=√(,9)⋅√(,7)*i

3√(,7)*i

Final Answer

√(,−63)=3*i√(,7)

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