1Cademy - Index of the Radical

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$n$ th Root of a Number

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Index of the Radical

In the radical notation $\sqrt[n]{a}$ , the number $n$ is called the index of the radical. The index specifies which root is being taken — it tells you the power to which some number must be raised to produce the radicand $a$ .

For a square root, the index is $2$ , but by convention it is not written: $\sqrt{a}$ means $\sqrt[2]{a}$ .
For a cube root, the index is $3$ : $\sqrt[3]{a}$ .
For a fourth root, the index is $4$ : $\sqrt[4]{a}$ .
For a fifth root, the index is $5$ : $\sqrt[5]{a}$ .

The index must be a positive integer greater than or equal to $2$ . Together with the radicand (the expression under the radical sign), the index completely determines the value of a radical expression.

Updated 2026-04-21

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