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 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 an extraneous solution?

Back

A solution that does not satisfy the original equation after it has been derived.

Front

How can you check for extraneous solutions?

Back

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

Front

Solve: √(x + 5) = 7

Back

x = 44.

Front

Solve: √(2x - 3) = 5

Back

x = 14.

Front

Solve: √(x - 1) + 3 = 6

Back

x = 10.

Front

Solve: √(x + 4) = -2

Back

No solution, as a square root cannot be negative.