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

What is the first step in solving a radical equation?

Back

The first step is to isolate the radical on one side of the equation.

Front

What happens when you square both sides of a radical equation?

Back

Squaring both sides eliminates the radical, but it can introduce extraneous solutions that must be checked.

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

How do 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 is the domain of a radical function?

Back

The domain of a radical function is the set of all input values (x) for which the expression under the radical is non-negative.

Front

What is the difference between even and odd roots in radical equations?

Back

Even roots (like square roots) can only yield non-negative results, while odd roots (like cube roots) can yield both positive and negative results.

Front

How do you solve a radical equation with multiple radicals?

Back

Isolate one radical, square both sides, and repeat the process until all radicals are eliminated.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions is crucial to ensure that no extraneous solutions are accepted as valid.