D. Radicals in Simplified Form

D. Radicals in Simplified Form

Because not every radical contains a perfect square or perfect cube radicand, it is important to know how to work with radicals in the cases when an exact value, rather than an approximate one, is required.

Radicals can be expressed in two different forms, as entire radicals and as mixed radicals. It is implied that the numerical coefficient in front of a radical is being multiplied by the radical.

Entire Radical a radical expression with all values sitting under the root sign Mixed Radical a radical expression, usually in simplest form, that has a numerical coefficient in front of the root sign and a value under the root sign Coefficient a number that a radical or variable is multiplied by; it is usually written in front.

Some examples of each form are included below.

Entire radicals can often be written as mixed radicals in simplified form. To express a radical in simplest form, any perfect nth root factors (perfect squares, perfect cubes, etc.) are removed from the radicand and placed as a coefficient of the radical. For instance , is an entire radical and is not expressed in simplest form. It can be expressed in simplest form by reducing to equal .

Simplified Form an expression written in exact, reduced form