Solving Radical Equations

Front

What is a radical equation?

Back

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

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, you can move all other terms to the opposite side of the equation.

Front

What is the first step in solving a radical equation?

Back

Square both sides of the equation to eliminate the radical.

Front

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

Back

Simplify the equation and solve for the variable.

Front

What is a potential issue when solving radical equations?

Back

Extraneous solutions may arise, which are solutions that do not satisfy the original equation.

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

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

Back

x = 25.

Front

Solve the equation √(x + 3) = 4.

Back

x = 13.

Front

What is the solution to the equation √(2x - 1) = 3?

Back

x = 5.

Front

How do you solve the equation √(x) + 2 = 5?

Back

Isolate the radical: √(x) = 3, then square both sides: x = 9.