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 and then square both sides to eliminate the radical.

Front

What is the first step in solving @@ \sqrt{n+3}=\sqrt{11-n}@@?

Back

The first step is to square both sides of the equation.

Front

What is the solution to @@ \sqrt{n+3}=\sqrt{11-n}@@?

Back

The solution is n = 4.

Front

What should you check after solving a radical equation?

Back

You should check for extraneous solutions by substituting the solution back into the original equation.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that does not satisfy the original equation after it has been derived.

Front

Solve the equation @@ \sqrt{5p+1}=\sqrt{2p+7}@@.

Back

The solution is p = 2.

Front

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

Back

Squaring both sides helps to eliminate the radical, allowing for easier manipulation of the equation.

Front

What is the solution to @@ \sqrt{t}=\sqrt{16}@@?

Back

The solution is t = 16.

Front

What happens if you square both sides of an equation incorrectly?

Back

Squaring both sides incorrectly can lead to incorrect solutions or extraneous solutions.