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

For some reason in my TI-83 if I just enter

it will yield

but if I do

, turn it back into the fraction

and then raise that to

it will give me the correct fraction

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

Same thing for

if I just try to raise this to ^(1/2) in the calculator it will yield 1.333 repeating, which equals

when converted back to a fraction. But if I do

it will yield .444 repeating, turn it back into the fraction

and then I can raise that to ^(1/2) to get the correct answer which is