Square Root Notation

In algebra, a square root usually appears in an expression like this:

In plain language, this means “the square root of is equal to ”.

Implied Index

The small number tucked into the radical is called the index, and it says which root to take. A square root leaves it out, so a bare radical always means the second root.

Both expressions mean the same thing but, in practice people, people rarely write the index. Every other root spells its index out: is the cube root, is the fourth root. See the radical notation for the general -th root.

Equivalent Notation

A root can also be written as an exponent. Taking the square root of an expression is the same as raising it to the one-half power.

So the expression at the top of this page has a second spelling.

The two forms are interchangeable. This site writes the radical when the point is “take a root” and the exponent when the root sits inside a larger chain of powers, where a fraction in the superscript is easier to combine with the exponents around it.

To calculate the square root of a number see this page.

Related Notation

In math, we use the √ symbol to represent the square root and the n-th root of an expression.

In mathematics superscript text is used to indicate the exponent of some number.