Roots are also known as radicalsRoots are sort of the opposite of exponents. So, you square 3 to get 9, the square root of 9 is 3. There are as many roots as there are powers. Most of the time, the GMAT has you work with square roots, but you may also see other roots. If you come upon a cube root or fourth root, you can recognise it by the radical sign, √.

Radicals can often be simplified. For example, if you come up with an answer of √98, you are not done yet. Think of the factors of 98 that are perfect squares. You know that 2×49 = 98, and 49 is a perfect square. Put these factors under the radical sign: √(2×49). Now you can extract the 49 from the square root sign because its square root is 7. The result is 7√2.

Properties of Radicals


Squaring and Square Roots

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.

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.