Solving Radical Equations

Front

What is a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

How do you isolate a variable in a radical equation?

Back

You can isolate the variable by performing inverse operations, such as squaring both sides to eliminate the square root.

Front

What is the first step in solving the radical equation √(x + 5) = 9?

Back

Square both sides to eliminate the square root: x + 5 = 81.

Front

What is the solution to the equation √(x) = 8?

Back

x = 64.

Front

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

Back

Isolate the variable and solve for it.

Front

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

Back

To ensure that the solutions do not produce extraneous results when substituted back into the original equation.

Front

What does it mean to have an extraneous solution?

Back

A solution that does not satisfy the original equation after it has been derived.

Front

How do you solve the equation 2√(x) = 16?

Back

First, divide both sides by 2 to get √(x) = 8, then square both sides to find x = 64.

Front

What is the first step to solve the equation √(2x + 3) = 5?

Back

Square both sides to eliminate the square root: 2x + 3 = 25.

Front

What is the solution to the equation √(x - 1) + 3 = 7?

Back

x = 10.