Irrational inequalities

Irrational inequalities are inequalities that involve expressions with roots (such as square roots, cube roots, etc.) of algebraic expressions. To solve them, you must consider both the inequality and the domain where the expressions under the roots are defined (i.e., where they are real numbers).

Important properties

• The expression under an even root (like a square root) must be non-negative.

• Squaring both sides of an inequality can introduce extraneous solutions; always check the solutions in the original inequality.

• The solution set is the intersection of the domain of the root and the solution to the transformed inequality.