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 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

Why is it important to check your solutions in radical equations?

Back

Some solutions may be extraneous, meaning they do not satisfy the original equation.

Front

Solve: √(x + 5) = 3

Back

x = 4.

Front

Solve: √(2a - 1) = 5

Back

a = 13.

Front

What does it mean if a radical equation has no solution?

Back

It means that there are no values for the variable that satisfy the equation.

Front

Solve: √(r + 1) = r - 1

Back

r = 2.

Front

What is an extraneous solution?

Back

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

Front

Solve: √(x - 2) + 1 = 4

Back

x = 17.