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, solve the resulting equation for the variable and check for extraneous solutions.

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

Solve the equation √(2x - 1) = 3.

Back

Square both sides: 2x - 1 = 9. Then, add 1 to both sides: 2x = 10. Finally, divide by 2: x = 5.

Front

What is the importance of checking 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

How do you solve the equation √(x + 4) - 2 = 0?

Back

Add 2 to both sides: √(x + 4) = 2. Then square both sides: x + 4 = 4, leading to x = 0.

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 happens if you have multiple radicals in an equation?

Back

If there are multiple radicals, isolate one radical at a time, square both sides, and repeat the process until all radicals are eliminated.