Powers and Roots of Numbers - Arithmetic - Math Review - GMAT Quantitative Review

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 kn, which means the nth power of k. For example, image and image 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 image denotes the positive number whose square is n. For example, image denotes 3. The two square roots of 9 are image and image.

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