Irrational equations

An irrational equation is an equation that contains the unknown variable inside a root (such as a square root or cube root). To solve such equations, we often isolate the root and then raise both sides to a suitable power to eliminate the root. However, this process can introduce extraneous solutions, so it is important to check all solutions in the original equation.

Important properties

• Irrational equations often involve roots with variables inside.

• Isolate the root before raising both sides to a power.

• Raising both sides to a power can introduce extraneous solutions.

• Always check potential solutions in the original equation.