A *n*th **root**, *r*, of a number *m*, is a number such that *r ^{n}* =

*m*. This is different from the root of a function – e.g. a root of a quadratic.

The *root* students most frequently come across, the **square root** (or 2nd root) *r*, of a number *m*, is a number such that *r*^{2} = *m*. For example, a square root of 25 is 5 because 5^{2} = 5 × 5 = 25. Note that −5 is another square root of 25, because (−5)^{2} = 25 also.

There is a mathematical symbol used for positive square roots:

\(\sqrt{25}=5\) which can be read as “the (positive) square root of 25 is equal to 5.”

In simpler terms: the square root of a number *m*, is the number that when squared (multiplied by itself), gets you the original number *m*.

The **cube root** (or 3rd root) *r*, of a number *m*, is a number such that *r*^{3} = *m*. For example, a cube root of 64 is 4 because 4^{3} = 4 x 4 x 4 = 64. The mathematical symbol for higher roots is similar to the square root symbol – but a number is added to the outside to show the type of root. For example, we could write \(\sqrt[3]{64}=4\).

*n*th roots of integers which are not perfect powers of *n* are surds.

**Relevant lessons:**