Parts of a Radical – Index, Radicand, Radical Sign

All 6 parts on the diagram

Show the list

All 6 parts 6

Coefficient The number multiplying the radical. It is 2 here, so the expression means 2 times the cube root of 27.
Index Which root to take: 3 here, a cube root. It is also called the degree. A square root has index 2, which is left unwritten.
Radical sign The √ shape that says take a root. Joined to the bar over the radicand, it makes the full radical symbol.
Vinculum The horizontal bar over the radicand. It shows exactly what is under the root.
Radicand The number you take the root of: 27 here.
Radical expression The whole expression containing the radical. This one equals 2 × 3 = 6, because 3 × 3 × 3 = 27.

How this list was compiled: Read 2026-09-26. Wikipedia, Nth root, https://en.wikipedia.org/wiki/Nth_root : the nth root of x written with the radical symbol, n called the index or degree and x the radicand; a root of degree 2 a square root, usually written with the degree omitted, and degree 3 a cube root; any expression containing a radical called a radical expression. Wikipedia, Vinculum (symbol), https://en.wikipedia.org/wiki/Vinculum_(symbol) : the vinculum as part of a radical marking the whole radicand; Descartes joining the radical sign √ with the vinculum to make the radical symbol used today. Wikipedia, Coefficient, https://en.wikipedia.org/wiki/Coefficient : a coefficient as a multiplicative factor in a term. The worked value 2 × 3 = 6 is checked: 3 × 3 × 3 = 27. Licence: own work

The drawing: Drawn for this site by script, 2026-09-26. Own work. Licence: own work

How it works

The parts of a radical on one expression, 2 times the cube root of 27: the coefficient in front, the index in the crook of the radical sign, the bar over the radicand, and the radicand itself.

Read the full guide

Reading it

The index says which root: 3 means cube root. The radicand, under the bar, is the number you take it of. The coefficient multiplies the result. Here the cube root of 27 is 3, because 3 × 3 × 3 = 27, and 2 × 3 = 6.

Square roots

A square root has index 2, but the 2 is left off. So √25 means the square root of 25, which is 5.

Work from the inside out: take the root of the radicand first, then multiply by the coefficient.

Questions and answers

What is the number inside a radical called?

The radicand. It is the number under the bar that you take the root of; in the cube root of 27, the radicand is 27.

What is the index of a radical?

The small number in the crook of the radical sign that says which root to take. It is also called the degree. A square root's index, 2, is usually not written.

What is the line over a radical called?

The vinculum. It extends the radical sign across the whole radicand, so it is clear what is under the root.