GMAT Quantitative Review
3.0 Math Review
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 kn, which means the nth 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 .