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 to eliminate the square root: (√(x + 3))^2 = 5^2.

Front

What do you do after squaring both sides of a radical equation?

Back

After squaring both sides, simplify the equation and solve for the variable.

Front

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

Back

The solution is x = 22, found by squaring both sides and then isolating x.

Front

Why is it important to check your solutions in radical equations?

Back

It's important to check solutions because squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

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 can you check if a solution is extraneous?

Back

To check if a solution is extraneous, substitute it back into the original equation to see if it holds true.

Front

What is the general form of a radical equation?

Back

The general form of a radical equation is f(x) = √g(x), where g(x) is a polynomial expression.

Front

What is the domain of a radical function?

Back

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