Evaluate square root of -98

Problem

√(,−98)

Solution

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

√(,−98)=√(,−1⋅98)

√(,−98)=i√(,98)

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

98=49⋅2

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

√(,98)=√(,49⋅2)

√(,98)=7√(,2)

4. Combine the results to express the final answer in terms of i

i√(,98)=7*i√(,2)

Final Answer

√(,−98)=7*i√(,2)

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