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 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 expression 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 produce non-negative results, while odd roots (like cube roots) can produce both positive and negative results.

Front

How do you solve the equation √(x + 3) = 5?

Back

Square both sides: x + 3 = 25, then solve for x: x = 22.

Front

What is the solution to the equation √(2x - 1) = 3?

Back

Square both sides: 2x - 1 = 9, then solve for x: x = 5.