Simplify square root of (3-2)^2+(-1-(-3)^2)

Problem

√(,(3−2)2+(−1−(−3)2))

Solution

1. Simplify the expression inside the first set of parentheses.

(3−2)=1

2. Evaluate the exponent inside the second set of parentheses.

(−3)2=9

3. Simplify the expression inside the second set of parentheses.

(−1−9)=−10

4. Substitute these values back into the original expression.

√(,1+(−10))

5. Square the first term and perform the addition.

1=1

1−10=−9

6. Evaluate the square root of the negative number using the imaginary unit i where i=√(,−1)

√(,−9)=√(,9)⋅√(,−1)=3*i

Final Answer

√(,(3−2)2+(−1−(−3)2))=3*i

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