Radical Equations Flashcard

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 isolate a radical in an equation?

Back

To isolate a radical, you can move all other terms to the opposite side of the equation, leaving the radical alone on one side.

Front

Back

The first step is to eliminate the fraction by multiplying both sides of the equation by the denominator.

Front

What is the principle of squaring both sides of an equation?

Back

Squaring both sides of an equation can eliminate a square root, but it may introduce extraneous solutions that need to be checked.

Front

Back

The solution involves isolating the radical and squaring both sides.

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, often due to the square root of a negative number.

Front

Back

The solution involves isolating the radical and squaring both sides.

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

Back

The solution involves isolating the radical and squaring both sides.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions ensures that the solutions found are valid and satisfy the original equation.