Prove if a belongs R, then (a^2)^1/2= |a|?

[hugo28]

Would you please help me? Thanks in advance.

Prove that if a belongs to R, then (a^2)^1/2 = |a|?
by using Abstract, Discrete, Algebraic Math.

I work, but stuck:
|a| =< (a^2)^1/2, then
- (a^2)=< a =< (a^2)

Please help!

 

[mathman]

Depends on your definition of square root. The usual definition means you will have two answers a and -a. However if you insist that the square root be positive, the |a| is the positive root.

 

[JSuarez]

If a >= 0, it's pretty much obvious; otherwise, consider -a.

 

[Hurkyl]

Thread closed for user not showing any work.