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 solve a radical equation?

Back

To solve a radical equation, isolate the radical on one side of the equation, then square both sides to eliminate the radical, and solve the resulting equation.

Front

What is the principal square root?

Back

The principal square root of a number is the non-negative root. For example, the principal square root of 9 is 3.

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 extraneous solution in radical equations?

Back

An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation.

Front

Example of a radical equation: Solve √(x + 3) = 5.

Back

x + 3 = 25; x = 22.

Front

What is the first step in solving √(2x - 1) = 3?

Back

Square both sides to eliminate the radical: 2x - 1 = 9.

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 happens if you square both sides of an equation incorrectly?

Back

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

Front

What is a cube root?

Back

A cube root of a number x is a number y such that y^3 = x.