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

Back

After squaring both sides, you should isolate the variable and solve the resulting equation.

Front

What is the importance of checking your solutions in radical equations?

Back

Checking solutions is important 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

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

Back

Square both sides: 2x + 1 = 9. Then, isolate x: 2x = 8, so x = 4.

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

How can you eliminate a cube root in an equation?

Back

To eliminate a cube root, you can cube both sides of the equation.

Front

Solve the equation: 3√(x - 2) = 6.

Back

Divide by 3: √(x - 2) = 2. Then square both sides: x - 2 = 4, so x = 6.