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

What is the first step in solving the equation @@ \sqrt{3y + 4} = 5@@?

Back

Square both sides.

Front

Back

x = 36.

Front

Back

z = 25.

Front

What does it mean to isolate the variable in an equation?

Back

To manipulate the equation so that the variable is on one side and all other terms are on the other side.

Front

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

Back

It allows you to eliminate the square root, but you must check for extraneous solutions.

Front

Back

n = 0.

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

Back

n = 4.

Front

What is the domain of a radical function?

Back

The set of all possible input values (x) for which the function is defined, typically requiring the expression under the radical to be non-negative.