Question 32745
Is sqrt x^2 = x an identity (true for all values of x)? Explain answer please?
IN MATHS AS A RULE/COVENTION WE TAKE SQRT(A) AS THE POSITIVE VALUE ONLY.THAT IS SQRT(4) IS TAKEN AS +2 ONLY.,THOUGH -2 IS ALSO POSSIBLE,UNLESS OTHERWISE INDICATED.
CASE 1....X IS POSITIVE
SO WE GET LHS=SQRT.(X^2)=+X

RHS =+ X...

SO WE HAVE X=X WHICH IS AN IDENTITY AS IT IS TRUE FOR ANY VALUE OF X.
CASE 2......X IS NEGATIVE 
SO WE GET LHS=SQRT.{(-X)^2}=SQRT.(X^2)=+X

RHS = -X...

SO WE HAVE X=-X WHICH IS NOT  AN IDENTITY AS IT IS TRUE FOR ONLY X=0