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 isolate a variable in a radical equation?

Back

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

Front

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

Back

The first step is to square both sides of the equation: (√(x + 3))^2 = 5^2, which simplifies to x + 3 = 25.

Front

What is the solution to the equation √(x + 3) = 5?

Back

After squaring both sides, you get x + 3 = 25. Subtracting 3 from both sides gives x = 22.

Front

What should you do after solving a radical equation?

Back

After solving a radical equation, always check your solution by substituting it back into the original equation to ensure it is valid.

Front

What is an extraneous solution?

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 can you identify extraneous solutions in radical equations?

Back

You can identify extraneous solutions by substituting the solutions back into the original equation and checking if they hold true.

Front

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

Back

The principle states that if two expressions are equal, squaring both sides will maintain the equality, but it may introduce extraneous solutions.

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

How do you solve the equation √(2x - 1) = 3?

Back

Square both sides: (√(2x - 1))^2 = 3^2, leading to 2x - 1 = 9. Then solve for x.