# Prove lim(sqrt(a(n)^2))=a^2

1. Sep 20, 2008

### LMKIYHAQ

1. The problem statement, all variables and given/known data
I am trying to prove that given an$$\geq$$0 for all n , and
lim(an=a), that lim(sqrt(a(n)^2))=a^2.

2. Relevant equations

3. The attempt at a solution
I have multiplied the bottom and top by the conjugate but I cannot find what to set as a lower bound for the absolute value of sqrt(an)+sqrt(a).

2. Sep 20, 2008

### tiny-tim

Hi LMKIYHAQ!

I don't get it … for an ≥ 0, sqrt(a(n)^2) = an, and so lim(sqrt(a(n)^2)) = a, doesn't it?

3. Sep 20, 2008

I agree with tiny-tim: whether you write it as

$$\lim_{n \to \infty} \sqrt{a_n^2}$$

or

$$\lim_{n \to \infty} \sqrt{a_n}^2$$

the limit certainly is not $$a^2$$.

4. Sep 20, 2008

### Unassuming

You mean

5. Sep 20, 2008

### LMKIYHAQ

Darn. I wrote the problem down wrong everybody. I am sorry, I hope you are all good enough s.t. you didn't spend much time thinking about that!! I am sorry.

How do I delete a thread?

P.S. i meant lim(sqrt(a(n)))=a(n), and I figured it out.