## GMAT Quantitative Review

## 3.0 Math Review

### 3.1 Arithmetic

### 7. Powers and Roots of Numbers

When a number *k* is to be used *n* times as a factor in a product, it can be expressed as *k ^{n}*, which means the

*n*th power of

*k*. For example, and are powers of 2.

Squaring a number that is greater than 1, or raising it to a higher power, results in a larger number; squaring a number between 0 and 1 results in a smaller number. For example:

A *square root* of a number *n* is a number that, when squared, is equal to *n*. The square root of a negative number is not a real number. Every positive number *n* has two square roots, one positive and the other negative, but denotes the positive number whose square is *n.* For example, denotes 3. The two square roots of 9 are and .

Every real number *r* has exactly one real *cube root*, which is the number *s* such that . The real cube root of *r* is denoted by . Since , . Similarly, , because .