Evaluate square root of 3^2-2^2-6^2

Problem

√(,3−2−6)

Solution

1. Evaluate the exponents inside the square root by squaring each integer.

3=9

2=4

6=36

2. Perform the subtractions in the order they appear under the radical.

9−4=5

5−36=−31

3. Identify the result as a square root of a negative number, which involves the imaginary unit i

√(,−31)=√(,−1⋅31)

4. Simplify the radical by extracting the imaginary unit.

√(,−1⋅31)=i√(,31)

Final Answer

√(,3−2−6)=i√(,31)

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