Solve 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 variable in a radical equation?

Back

To isolate a variable in a radical equation, you can square both sides of the equation to eliminate the radical, then solve for the variable.

Front

What is the first step in solving the equation √(x) = 3?

Back

The first step is to square both sides of the equation to eliminate the square root, resulting in x = 9.

Front

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

Back

The solution is x = 9.

Front

What should you check after solving a radical equation?

Back

You should check your solutions by substituting them back into the original equation to ensure they do not create extraneous solutions.

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 solve the equation √(x + 5) = 8?

Back

Square both sides to get x + 5 = 64, then solve for x to find x = 59.

Front

What is the solution to the equation √(x - 2) = 4?

Back

The solution is x = 18.

Front

What is the general form of a radical equation?

Back

The general form of a radical equation can be expressed as √(f(x)) = g(x), where f(x) and g(x) are functions of x.

Front

What happens if you square both sides of an equation incorrectly?

Back

Squaring both sides incorrectly can lead to incorrect solutions or extraneous solutions.