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 solve a radical equation?

Back

To solve a radical equation, isolate the radical on one side of the equation, then square both sides to eliminate the radical. Check for extraneous solutions afterward.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving an equation but does not satisfy the original equation.

Front

Solve the radical equation: √(x + 5) = 3

Back

x = 4

Front

Solve the radical equation: √(2x - 1) = 5

Back

x = 13/2

Front

Solve the radical equation: √(x - 2) + 3 = 7

Back

x = 7

Front

Solve the radical equation: √(x + 1) = x - 3

Back

x = 4 (check for extraneous solutions).

Front

What is the first step in solving the equation √(x) = 4?

Back

Square both sides to eliminate the radical: x = 16.

Front

What should you do after solving a radical equation?

Back

Always check your solutions by substituting them back into the original equation.

Front

Solve the radical equation: √(x + 3) = x - 1

Back

x = 2 (check for extraneous solutions).