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