Solve 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

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

Square both sides to get x + 3 = 25.

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

Solve the equation √(x - 1) = 3. What is x?

Back

x = 10.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

How do you solve the equation √(2x + 4) = 6?

Back

Square both sides to get 2x + 4 = 36, then solve for x to get x = 16.

Front

What is the solution to the equation √(x + 5) = 7?

Back

x = 44.

Front

If you have the equation √(x) + 2 = 6, how do you solve for x?

Back

Isolate the radical: √(x) = 4, then square both sides to find x = 16.