## Index of a Radical

### The index of a radical refers to the number written as a small number to the left of the square root sign (√)

The index of a radical refers to the number written as a small number to the left of the square root sign (√). It indicates the degree or power of the root.

For example, if we have √x, the index is 2. This means we are taking the square root of x.

Similarly, if we have ∛x, the index is 3. This means we are taking the cube root of x.

In general, if we have the radical √n√x, the index is n. This means we are taking the nth root of x.

The index determines how many times we need to multiply a number by itself to obtain the value inside the radical. For instance, if we have √16, the index is 2. We need to find a number that, when multiplied by itself, equals 16. In this case, that number is 4 because 4 × 4 = 16.

It’s important to note that the most common index is 2 (for square root), but other indices can also be used depending on the problem or context.

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