Solving Radical Equations

Front

What is a radical equation?

Back

An equation that involves a variable within a radical (square root, cube root, etc.).

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, perform algebraic operations to get the radical on one side of the equation by itself.

Front

What is the first step in solving the equation (2x - 5)^(1/3) = 3?

Back

Cube both sides of the equation to eliminate the cube root.

Front

What is the solution to the equation (2x - 5)^(1/3) = 3?

Back

x = 16.

Front

What does it mean to check for extraneous solutions?

Back

To verify if a solution obtained from an equation is valid by substituting it back into the original equation.

Front

What is a rational exponent?

Back

An exponent that can be expressed as a fraction, where the numerator is the power and the denominator is the root.

Front

How do you solve an equation with a rational exponent?

Back

Rewrite the equation using radical notation or raise both sides to the power of the denominator.

Front

What is the solution to the equation x^(1/2) = 4?

Back

x = 16.

Front

What is the importance of squaring both sides of an equation?

Back

Squaring both sides can eliminate square roots, but it may introduce extraneous solutions.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving an equation but does not satisfy the original equation.