Solving Radical Equations Review

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Front

How do you solve a radical equation?

Back

To solve a radical equation, isolate the radical on one side of the equation, then square both sides to eliminate the radical. Check for extraneous solutions afterward.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

Solve the radical equation: √(x + 3) = 3. What is x?

Back

x = 6.

Front

Solve the radical equation: √(2x - 1) = 5. What is x?

Back

x = 13.

Front

What should you do after solving a radical equation?

Back

Always check your solutions by substituting them back into the original equation to ensure they are valid.

Front

Solve the radical equation: √(x^2 - 4) = 2. What are the solutions?

Back

x = 6 and x = -6.

Front

What is the first step in solving the equation √(x + 1) = x - 1?

Back

Isolate the radical: √(x + 1) = x - 1.

Front

Solve the radical equation: √(x + 2) = x. What are the solutions?

Back

x = 2.

Front

What happens if you square both sides of an equation incorrectly?

Back

Squaring both sides incorrectly can introduce extraneous solutions that do not satisfy the original equation.