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 on one side of the equation.

Front

What should you do after isolating the radical?

Back

After isolating the radical, square both sides of the equation to eliminate the radical.

Front

Why is it important to check your solutions in radical equations?

Back

It's important to check solutions because squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

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) = 9?

Back

Square both sides: x + 5 = 81, then solve for x: x = 76.

Front

What is the solution to the equation √(2x - 3) = 5?

Back

Square both sides: 2x - 3 = 25, then solve for x: x = 14.

Front

What happens if you have a radical equation like √(x) = -3?

Back

There is no solution because the square root of a number cannot be negative.

Front

How do you solve the equation √(x + 4) = x - 2?

Back

Square both sides: x + 4 = (x - 2)², then solve for x and check for extraneous solutions.