Write the expression in radicant exponent the given is square root of 81 what is the answer and the solution.

Use the square root key. For roots of higher index, use the xRoot key; the shifted function of the Y^x or [^] with exponent 1/3 for cube root, 1/4 for 4th root, or 1/n for the n-th root.

To calculate radicals use the square root key. For higher index roots use [SHIFT][X^y]. You need to enter the index before pressing the key. Or use the general power key but with exponent (1/n) where n is the index of the root.

Unfortunately this calculator does not display results in radical form. If you enter SQRT(147) you get 12.12435565...
What you are asking for is called rationalizing an irrational expression. Usually one tries to get rid of radicals that appear in the denominators. Here is an example.
Suppose you have 1/(c+SQRT(d)), and you want to get rid of the radical in the denominator. How to do it?
Recall the identity (a-b)*(a+b)= a^2-b^2. It is true for any a and b

Rationalizing a denominator (usual case)
Now consider (c+SQRT(d)). Multiply it by (c-SQRT(d))
[c+SQRT(d)]*[c-SQRT(d)]=c^2 -[SQRT(d)]^2=c^2-d
You see that there is no radical.
Now take 1/(c+SQRT(d)). To get rid of the radical from the denominator multiply it by (c-SQRT(d)). But to leave the value of your expression 1/(c+SQRT(d)) unchanged, you must multiply both numerator and denominator by (c-SQRT(d)).
The numerator becomes 1*(c-SQRT(d))=c-SQRT(d), and the denominator (c^2-d).
Finally, the rationalized form of the expression 1/(c+SQRT(d)) is
[c-SQRT(d)]/[c^2-d].

Rationalizing a numerator
Sometimes, people have a radical in the numerator that they want to get rid of and have it in the denominator. The procedure is the same
Example:(c+SQRT(d)), the denominator here is 1
(c+SQRT(d))=(c+SQRT(d))*[c-SQRT(d)]/[c-SQRT(d)]. This gives
[c^2-d]/[c-SQRT(d)]
You have no radical in the numerator but there is one in the denominator. This is called rationalizing the numerator.
Your case is a lot simpler
SQRT(147)=7*SQRT(3)
Multiply it by SQRT(3)/SQRT(3) which is 1. This gives
SQRT(147)=7*3/SQRT(3)=21/SQRT(3)

SQRT(147)= 21/SQRT(3)

The capability of these calculators to handle irrational numbers in radical form is limited to square roots. Roots of index other than 2 are always displayed in their decimal representation.
If the calculator IO mode is set to MathIO, square roots will be displayed with the radical symbol. More complicated expressions with square roots might not be preserved and will be given as decimal numbers.

On your calculator, in the 4th column and third row down you should see the root x symbol. In order to do a radical, just press a number and then press the root x and you shall get the square root of your number. Now in order to do this for cubed root, fourth root, etc, you have to hit the number you want to put in the radical, the 2nd key, look for the y^x key in the last column second row, and then the number outside the radical. For example, if you wanted to do the cubed root of 8, you would hit 8, 2nd y^x, 3, and you should get 2.

SQRT(81), here use the symbol that looks like a V, the radical
The other way is (81)^(1/2) where [^] is the general power key.

Use the xth-root function to compute any root. It's the fifth entry on the MATH menu, which you can get by pressing the MATH key. The fourth entry on the same menu gives you the third root without needing the 3 to be specified.

For example, to compute the 5th root of 32, press 5 MATH 5 3 2 ENTER.

You can perform coordinate conversions in the COMP, STAT, MATRIX and VECTOR Modes.
Angle unit may be in either degree or radian.

To convert from rectangular to polar, (SQRT(2)/2,SQRT(2)/2)

Press [SHIFT] [+] (Pol)
Screen displays Pol(
Type in SQRT2
Use right arrow to move cursor out of radical
Type in /2 [SHIFT] [,]
Type in SQRT2
Use right arrow to move cursor out of radical
Type in /2
Close the right parenthesis
Screen displays Pol (SQRT2 /2, SQRT2 / 2)
Press [=]. Display echoes the command on top line and result in bottom line as r=1, theta =45, (if unit is in degree) or theta = 0.7853981634 if unit is radian.

To convert from polar to rectangular coordinates
Note: You cannot use the answer memory to convert back to rectangular because the calculator will use the r-value only. So you will have to enter the radius AND the angle.

ex: Rec(1,45)
Angle must be in degree
Press [SHIFT][-] (Rec)
Screen display Rec(
Type in 1 [SHIFT] (,) 45 [)] [=]
Calculator displays X=0.7071067812, Y=0.7071067812
If you press the SD key hoping to convert the decimals to radicals, the calculator will not do it.

As to the "confusion", I have found none.
After you finish entering the argument of a square root, use the right arrow to move cursor out of under the root symbol to signify that the argument is complete. If you use a left parenthesis inside the root, you must insert the matching right parenthesis inside the root, then move cursor outside the root.

This is how the calculator behaves, and I am not expressing an opinion on how simple or complicated that is. I assume that to make full use of the calculator capabilities, one has to converse with it, using the syntax it understands.

The key to use for the square, and the cube are well marked and they share the same physical key (X to 2) or [SHIFT][X to 2]. Similarly the keys to use for the square root and the cube root share the same physical location (the square root key, to the right of the square key).

For any other exponent, including fractions and negative exponents you use the universal power key labeled [X to ] ( X with a raised square).

1. You enter the base (the number to be raised to a power).
2. You press the [X to ] power key.
3. You close the parenthesis (the right one).
4. You press [=]

Sometimes the result may not be displayed as a decimal number, but as a radical (if you take a root). To make sure it is displayed as a decimal number, in step 4 above, press [SHIFT][=]

Sorry to disappoint you. You can enter a radical by making use of the square root or the universal power [^] with fractionary exponent, but once you press the [ENTER] key, your expression is calculated and displayed as a decimal number.
By updating the OS to version 2.53MP, you will be able to manipulate fractions more easily than your current OS version, but no facility is provided for radicals.