Solving Radical Equations with some Extraneous solutions

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

How do you identify extraneous solutions in radical equations?

Back

To identify extraneous solutions, substitute the potential solutions back into the original equation to see if they hold true.

Front

What is the first step in solving a radical equation?

Back

Isolate the radical expression on one side of the equation.

Front

What happens when you square both sides of a radical equation?

Back

Squaring both sides eliminates the radical but may introduce extraneous solutions.

Front

Solve the radical equation: √(x + 4) = 6

Back

x = 32.

Front

Solve the radical equation: √(2x - 1) = 3

Back

x = 5.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions ensures that they are valid and not extraneous.

Front

Solve: √(x + 9) = 5

Back

x = 16.

Front

Solve: √(x - 3) + 2 = 5

Back

x = 7.

Front

What is the definition of a radical equation?

Back

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