Evaluate square root of -96

Problem

√(,−96)

Solution

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

√(,−96)=√(,−1⋅96)

√(,−96)=i√(,96)

2. Factor the radicand to find the largest perfect square divisor.

96=16⋅6

3. Apply the product property of square roots to separate the perfect square.

i√(,96)=i√(,16⋅6)

i√(,96)=i√(,16)⋅√(,6)

4. Simplify the square root of the perfect square.

√(,16)=4

i⋅4⋅√(,6)=4*i√(,6)

Final Answer

√(,−96)=4*i√(,6)

Want more problems? Check here!