When I type in (0.02) to the power of 2, it displays E. I want decimals

There is no problem, see captured image below:

Press MODE then select "Normal" on the top line.

The square root of 148 is 2*sqrt(37), the square of 3*sqrt(12) is 108, but that's not the point.

The TI-84 can't produce results like 2*sqrt(37). It can produce results as fractions but not involving roots. Some other machines, like the TI-89 can, but not the 84.

Sorry if that wasn't the answer you were hoping for.

You apparently have your calculator set to display no digits to the right of the decimal point. 5/2 is 2.5, which rounds to 3, and 50/100 is 0.5, which rounds to 1.

To change the display setting, press MODE, highlight the desired settings on the first two lines, then press ENTER followed by 2ND QUIT. Try setting "NORMAL" and "FLOAT" and see what results you get now.

Here is screen capture of the calculation, performed on TINspire with TI 84 plus keyboard.To type in the imaginary unit use key sequence [2nd][dot], do not use [ALPHA][X^2] for the letter I.
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well,

I really don't like to tell this to you but the Ti-84 plus will not display a square root as an answer, it will always return answers in decimal form. The best way for you to simplify roots is by using a factor tree and knowing your squares up to 30. I went through all of that using a ti-83 plus so I completely understand your desire for it to show a root, it just won't. I really wish you the best with this problem, but having read the owners manual for it, I just don't see any other way to do it.

No, is giving you the correct result. When you negate 3-squared, you should get -9. If you want to square negative three, you need to type it in as ( (-) 3 ) ^ 2 or ( (-) 3 ) x^2

There is a difference between (-3)^2 and -(3^2). If you omit the parentheses, the calculator will interpret it as the latter.

If in doubt, use parentheses.

Unfortunately, you can't. From the manual:

If [...] the answer cannot display in 10 digits (or the absolute value is less than 0.001), the TI-84Plus expresses the answer in scientifc notation.

I am afraid I do not completely understand what you want. This calculator does not have a Computer Algebra System or CAS. So the results of all calculations will be displayed as decimal numbers, and that includes the square and other roots that are irrational numbers (square root of 2, 3, 5 7, etc.)

You cannot manipulate radicals on this calculator, whether for small numbers or large numbers. Sorry.

Enter the fraction for example: enter 8/12.
The answer will be .666666
Then click Math (which is located under the Alpha button).
Click the ->Frac button (the first one).
It should come up as Ans->Frac.
Click Enter.
It should now read 2/3 which is 8/12 reduced.
Note: I have a TI-84 Plus Silver Edition, and the TI-84 Plus might not have this function, but that is how I do it on my TI-84 Plus Silver Edition