We just saw that roots express fractional exponents. But it is ofteneasier to work with roots in a different format. When a number or termis raised to a fractional power, the expression can be converted intoone involving a root in the following way:
with the
sign as the radical sign, and
as the radicand.
Roots are like exponents, only backward. For example, to square the number 3 is to multiply 3 by itself: 32 = 3
3 = 9. The root of 9,
, is 3. In other words, the square root of a number is the number that, when squared, is equal to the given number.
Square roots are the most commonly used roots, but there are also cube roots (numbers raised to 1⁄3),fourth roots, fifth roots, etc. Each root is represented by a radicalsign with the appropriate number next to it (a radical without anysuperscript denotes a square root). For example, cube roots are shownas
, fourth roots as
, and so on. These roots of higher de
grees operate the same way square roots do. Because 33 = 27, it follows that the cube root of 27 is 3.
Here are a few examples:
The same rules that apply to multiplying anddividing exponential terms with the same exponent apply to roots aswell. Look for yourself:
Just be sure that the roots are of the samedegree (i.e., you are multiplying or dividing all square roots or allroots of the fifth power).
