Understanding the Concept of the nth Root in Mathematics: A Guide to Calculation and Application

nth root of a

The nth root of a number refers to finding the number that, when raised to the power of n, equals the given number

The nth root of a number refers to finding the number that, when raised to the power of n, equals the given number. In other words, it is the inverse operation of exponentiation.

To find the nth root of a number, you can use the following formula:

nth root of a = a^(1/n)

Where “a” represents the given number and “n” represents the index or the root you want to find.

For example, let’s say you want to find the cube root of 27. In this case, “a” would be 27, and “n” would be 3 since you want to find the cube root. Applying the formula:

Cube root of 27 = 27^(1/3)

To simplify further, remember that raising a number to the power of 1/n is the same as taking the nth root of the number.

Cube root of 27 = (27)^(1/3) = 3

So, the cube root of 27 is 3.

Another example: Let’s find the 4th root of 16.

4th root of 16 = 16^(1/4)

Now, let’s simplify further:

4th root of 16 = (16)^(1/4) = 2

So, the 4th root of 16 is 2.

It is important to note that the nth root of a number can be both positive and negative, except when n is even. For even roots, the result will only be positive.

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