GF: 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 + 5) = 7?

Back

Square both sides to get x + 5 = 49.

Front

What are extraneous solutions in radical equations?

Back

Solutions that do not satisfy the original equation after it has been solved.

Front

How can you check if a solution is extraneous?

Back

Substitute the solution back into the original equation to see if it holds true.

Front

Solve the equation √(x - 3) = 4.

Back

x = 19.

Front

What is the solution to the equation √(2x + 1) = 5?

Back

x = 12.

Front

How do you solve the equation √(x + 2) + 3 = 7?

Back

x = 7.

Front

What is the importance of squaring both sides in radical equations?

Back

It helps to eliminate the radical, making the equation easier to solve.

Front

Solve the equation √(x + 4) = x - 2.

Back

x = 6.