Evaluate square root of -294

Problem

√(,−294)

Solution

1. Identify the imaginary unit by using the property √(,−a)=i√(,a) for any positive real number a

√(,−294)=i√(,294)

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

294=49×6

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

i√(,49×6)=i√(,49)×√(,6)

4. Simplify the square root of the perfect square.

i√(,49)×√(,6)=7*i√(,6)

Final Answer

√(,−294)=7*i√(,6)

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