The nth root is unstoppable. You must sit back and wait. Hopefully you will survive it as it takes its deadly course.

rearrange the following: A^(1/n)= the nth root of A. eg A to the power 1/2 equals the square root of A. A to the power 1/3 equals the cube root of A. etc.

You can't prove this proposition because it isn't true.

Proof: the fifth root of 1024 is 4, and 4 is not irrational.

It is true that, when N is an integer greater than 1, the Nth root of any integer greater than 1 is either an integer orirrational, but that's a different matter.

only the number 1 (one)because it is perfect nth root .

The nth root of a number is that number which when raised to the nth power (ie when multiplied by itself n times) results in the number.

When n=2, it is the square root of the number;

when n=3 it is the cube root of the number.

To find the nth root of a number, an electronic calculator can be used, using the nth root button [x√y] (though more recent calculators replace the x and y by boxes) viz:

<n> [x√y] [2] [4] [4] [=]

or with the more recent calculators:

[#√#] <n> [Navigate →] [2] [4] [4] [=]

where <n> is the nth root, eg for 2nd root (square roots) enter [2];

and the # is being used to represent a box on the keys of the more recent calculator.

Considering the rules for indices, the nth root is the the number to the power of 1/n, ie 244^(1/n), thus the calculation can be done using the power button:

[2] [4] [4] [^] [(] [1] [÷] <n> [)] [=]

With the more recent calculators, the power button is pressed first, the 244 entered, the navigate-right key pressed (to get in to the power part of the input) and then the n entered.