Solving Radical Equations

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, and solve the resulting equation.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions is important because squaring both sides of an equation can introduce extraneous solutions that do not satisfy the original equation.

Front

What does it mean if a radical equation has no solution?

Back

A radical equation has no solution if the expression under the radical is negative, leading to an impossible situation when trying to find real number solutions.

Front

Example of a radical equation: √(x + 3) = 5. What is the solution?

Back

x = 22.

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 check if a solution is valid for a radical equation?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

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

Back

Square both sides to eliminate the radical: 2x - 1 = 9.

Front

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

Back

Squaring both sides incorrectly can lead to incorrect solutions or extraneous solutions.

Front

Solve the radical equation: √(x + 4) = 2. What is the solution?

Back

x = 0.