5. Solving Radical Equations

Front

Define 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

Back

Front

Solve the equation @@ ext{-7} oot{4}{m+1}=14@@.

Back

No Solution, since the left side cannot be negative.

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 the equation @@ oot{63-2x}=x@@.

Back

Front

What is the importance of checking solutions in radical equations?

Back

To ensure that the solutions do not produce extraneous results when substituted back into the original equation.

Front

Solve the equation @@ oot{5y-15}=y-3@@.

Back

Front

What is an extraneous solution?

Back

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

Front

Solve the equation @@17-2 oot{3x+10}=1@@.

Back

Front

What is the general method for solving radical equations?

Back

1. Isolate the radical. 2. Raise both sides to the power that eliminates the radical. 3. Solve the resulting equation. 4. Check for extraneous solutions.