Operations with Radicals

Simplifying Radicals

Simplifying a radical is putting the expression into its simplest possible form. This can be done to radicals through turning them into mixed radicals, where the radicand is divided by its greatest square factor, which is then removed and turned into a coefficient.

Examples:

√(72) = √(36.2) = 6√(2)

√(147) = √(49.3) = 7√(3)

∜(c⁹) = ∜(c⁴⋅c⁴⋅c¹) = c²∜(c)

√(48ab) = √(16⋅3⋅a²⋅a²⋅a²⋅b²⋅b²⋅b²⋅b²⋅b¹) = 4⋅a³⋅b⁴√(3b)

Adding and Subtracting Radicals

In order to add or subtract radicals, the index must be the same for each one. So, they must be simplified into this form before being added or subtracted.