The word "radical" comes from a Latin word (radix) meaning "root" (e.g., square root, cube root, etc.). You can always identify a radical equation by the "root" symbol (√).

Root numbers are shown in front of the radical. The exception is the square root, which is so common that the root "2" is not shown.

Radical functions can be transformed using the same transformation techniques we learned in the other function families.

Square root functions are inverses of quadratics, and cube root functions are inverses of cubics.

Radicals can be written in two basic forms, and we will need to convert back and forth between these in order to make simplifying easier.

• Radical form (using the root symbol)

• Exponent form (a rational exponent is shown)

Variables in exponent form can be simplified using a set of power rules, such as:

• Product of Powers

• Quotient of Powers

• Power to a Power

• Zero Power

• Negative Powers

To solve radical equations, we essentially try to raise both sides of the equation to the inverse power to remove the radical symbol and convert it back to one of the other function families. However, once we remove the radical(s), we have changed the equation so fundamentally that the solutions we arrive at may sometimes be "false." We call these false solutions, extraneous solutions. Extraneous solutions are those that do NOT satisfy the original equation when plugged back in.