How to find the base r? $\sqrt{144_r} = 12_r$ 
What is r?
The method I used is:
$\sqrt{ ((1 × r^2) + (4 × r^1) + (4 × r^0))} = ((1 × r^1) + (2 × r^0))$
and I tried solving this equation but I got now where.
the solution to this question according to the book is $r\geq 5$.

Simplify the expression first (remember that $r^0 =1$):
$$\sqrt{r^2+4r+4}_r = (r+2)_r$$
$$\sqrt{(r+2)^2}_r = (r+2)_r$$
$$(r+2)_r = (r+2)_r$$
What's wrong with this statement:
"This equality is true when $r ≥ -2$, because the square root of a real number is imaginary. Therefore, it is true for all (positive) bases."?
Hint: Look at the digits of the number in base $r$. For example, in base $2$, can we have the number $1323$?
