Evaluate square root of -72

Problem

√(,−72)

Solution

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

√(,−72)=√(,72)⋅√(,−1)

√(,−72)=√(,72)*i

2. Factor the radicand to find the largest perfect square divisor of 72

72=36⋅2

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

√(,72)*i=√(,36⋅2)*i

√(,72)*i=√(,36)⋅√(,2)*i

4. Simplify the square root of the perfect square.

√(,36)=6

6⋅√(,2)*i=6*i√(,2)

Final Answer

√(,−72)=6*i√(,2)

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