Vocabulary
Radical Equation- An equation with one or more radicals that have variables in their radicands.
Extraneous Solution- An apparent solution that must be rejected because it does not satisfy the original equation.
Extraneous Solution- An apparent solution that must be rejected because it does not satisfy the original equation.
Essential Information
Solving Radical Equations
Equations with radicals that have variables in their radicands are called radical equations.
Steps to solve a radical equation:
Equations with radicals that have variables in their radicands are called radical equations.
Steps to solve a radical equation:
- Isolate the radical on one side of the equation, if necessary.
- Raise each side of the equation to the same power to eliminate the radical and obtain a linear, quadratic, or other polynomial equation.
- Solve the polynomial equation.
Rational Exponents
When an equation contains a power with a rational exponent, the equation can be solved using a procedure similar to the one for solving radical equations. The power should first be isolated and then each side raised to the reciprocal of the rational exponent.
Extraneous Solutions
Raising each side of an equation to the same power may introduce extraneous solutions. When this procedure is used, each apparent solution should be checked in the original equation.
When an equation contains a power with a rational exponent, the equation can be solved using a procedure similar to the one for solving radical equations. The power should first be isolated and then each side raised to the reciprocal of the rational exponent.
Extraneous Solutions
Raising each side of an equation to the same power may introduce extraneous solutions. When this procedure is used, each apparent solution should be checked in the original equation.
Squaring Twice
When an equation contains two radicals, each side may need to be squared twice in order to eliminate both radicals.
When an equation contains two radicals, each side may need to be squared twice in order to eliminate both radicals.