Originally Posted by

**allyourbass2212** What I have been doing is just taking the number or fraction and raising it to ^(1/2) to find the difference of squares and it has worked for every problem except this one, and it seems to be a fault with the calculator.

For instance

$\displaystyle \frac{16}{81}x^4-16=(\frac{4}{9}x^2-4)(\frac{4}{9}x^2+4)=(\frac{2}{3}x-2)(\frac{2}{3}x+2)(\frac{4}{9}x^2+4)$

For some reason in my TI-83 if I just enter $\displaystyle \frac{16}{81}^{1/2}$ it will yield $\displaystyle \frac{16}{9}$

but if I do $\displaystyle \frac{16}{81} = .1975308642$, turn it back into the fraction $\displaystyle \frac{16}{81} $ and then raise that to $\displaystyle ^{1/2}$ it will give me the correct fraction $\displaystyle \frac{4}{9}$

Very strange indeed, anyone know why the calculator might be doing this?

Same thing for $\displaystyle \frac{4}{9}$ if I just try to raise this to ^(1/2) in the calculator it will yield 1.333 repeating, which equals $\displaystyle \frac{4}{3}$ when converted back to a fraction. But if I do $\displaystyle \frac{4}{9}$ it will yield .444 repeating, turn it back into the fraction $\displaystyle \frac{4}{9}$ and then I can raise that to ^(1/2) to get the correct answer which is $\displaystyle \frac{2}{3}$