Answer:They all need to be equal in both sides.Step-by-step explanation:a) sqrt(x^12)=x^6Take the square root --> x^6=x^6 b) sqrt(x^2-12x+36)=6-xFactor --> sqrt((x-6)(x-6))=6-xTake the square root --> x-6 = to 6-xThis is true since the square root gives you always a positive and a negative answer. c) sqrt(x^4+2x+1)=x^2+1Factor --> sqrt((x^2+1)(x^2+1))=x^2+1d)sqrt((x^2)/4+2x+4)= -(x)/2-2Simplify Factoring: In this part you can use the Quadratic Formula.--> sqrt((x/2+2)^2)=-(x)/2-2Take the square root --> (x/2)+2=-(x)/2-2This is true since the square root gives you always a positive and a negative answer.