SOLUTION: Need help understand these. 2) Is ( square root of x)^2=x an identity (true for all nonnegative values of x)? Answer: Explain your answer in this space.

Algebra ->  Radicals -> SOLUTION: Need help understand these. 2) Is ( square root of x)^2=x an identity (true for all nonnegative values of x)? Answer: Explain your answer in this space.       Log On


   

Question 36954: Need help understand these.
2) Is ( square root of x)^2=x an identity (true for all nonnegative values of x)?
Answer:
Explain your answer in this space.
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
%28sqrt%28x%29%29%5E2=x is an identity.

ILLUSTRATION:
Suppose x = 8, then sqrt%28x%29 = sqrt%288%29 = either 2sqrt%282%29 or -2sqrt%282%29.
Now, as both %282sqrt%282%29%29%5E2 and %28-2sqrt%282%29%29%5E2 are equal to 8 (= x) hence the truth of the statement made above can easily be verified.

However, if x be a negative number, say, x = -4.
Then sqrt%28-4%29 is imaginery and equals 2i [where i = sqrt%28-1%29]. So %28sqrt%28x%29%29%5E2 = %282i%29%5E2 = 4i%5E2 = -4 = x.
Thus, the proposition is also valid for negative real values of 'x'.