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

What should you do after squaring both sides of a radical equation?

Back

Simplify the equation and solve for the variable.

Front

What is a potential issue when solving radical equations?

Back

Squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

Front

How can you check if a solution is valid in a radical equation?

Back

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

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

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: √(v) = 3. What is v?

Back

v = 9.

Front

Solve: √(a + 2) = 4. What is a?

Back

a = 14.