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 isolate a variable in a radical equation?

Back

To isolate a variable in a radical equation, you typically square both sides of the equation to eliminate the radical, then solve for the variable.

Front

What is the first step in solving the radical equation √(x + 3) = 5?

Back

The first step is to square both sides of the equation: x + 3 = 25.

Front

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

Back

A radical equation has no solution if the operations performed lead to a contradiction, such as a negative number under a square root.

Front

Solve the radical equation √(x - 1) = 3 and check your solution.

Back

x = 10; Check: √(10 - 1) = √9 = 3.

Front

What is the extraneous solution in radical equations?

Back

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

Front

How do you check if a solution is valid in a radical equation?

Back

To check if a solution is valid, substitute it back into the original equation to see if both sides are equal.

Front

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

Back

x = 4; Check: √(2(4) + 4) = √12 = 4.

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all input values (x) for which the expression under the radical is non-negative.

Front

What is the importance of squaring both sides in radical equations?

Back

Squaring both sides helps eliminate the radical, allowing for easier manipulation and solving of the equation.