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I can not find the solutions to the following problems using 2 methods: algebraically and geometrically.

1. X with the square root of 2 =9

2. X with the square root of 3 =27

3. X with the square root of 4 =27
--Note: Fourth root

I'm not sure what you mean by "1. X with the square root of 2 =9".
Do you mean x^(1/2) = 9? If so then square both sides. If not, then please clairify.
"2. X with the square root of 3 =27 " means
x^(1/3) then cube both sides. If you meant to say x^3 then you have the terminology wrong, that would be x cubed, not x to the 1/3.
In any event, I'm not at all sure what your terminology means and I'm only guessing.

The problem was x with the square root of 2=9

x with the square root of 3=27, and the last one x with the square root of 4=27

Maybe, that why I don't understand them.

Do you mean sqrt(x)=9? third-root(3)=27? fourth-root(x)=27?
If so this is how we would write them
1. x^(1/2) = 9
square both sides to get x = 81
2. x^(1/3) = 27
cube both sides to get x = 27^3
3. x^(1/4) = 27
raise both sides to the 4th power to get x = 27^4
I think the symbol you're referring to is the radicand, it's the little check mark with a bar that goes over a number. When we put a number outside of it that's the root we want to find. When there's no number it indicates the square root, or simply the root of the number
This is what the 3rd root of X looks like.
v X

here's the 4th root
v X

I think this is what you mean, but you'll have to tell me if it isn't.

It was written with a 2 at the top of the x=9. I can not place the 2 above the x on this computer.

I think the answer would be 3 square, but I am not sure. Thank you if you can help.

yes, we express exponents using this symbol ^ (it's above the 6 on your keyboard), so x^2=9 is +/-3
If you meant x^3=27 that would be 3 also. x^4=27 would be the 4th root of 27.

I came up with the same answer for the first two problems, but I don't understand the 3rd problem , x^4=27, what is the 4th root of 27.

It would be the number who's product of itself 4 times is 27.
x^4=27 means x is approximately 2.27950... where the dots mean the number goes on forever.
Are you sure the problem wasn't x^4=81? That would be 3 also in that case.

You are so correct, the problem was x^4=16. Thanks, very much. I now see where I was going wrong.

x^4=16 means x=2 since 2^4 = 2*2*2*2 = 16

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