Solving Radical and Absolute Value Equations

Front

What is the first step to solving Radical Equations?

Back

Isolate the radical on one side of the equation.

Front

What is the opposite of a square root (\(\sqrt{ }\))?

Back

Squaring.

Front

What is the first step to solving: \(3\sqrt{3x-4}+5=1\)?

Back

Subtract 5 from both sides.

Front

What is the opposite of a cube root (\(\sqrt[3]{ }\))?

Back

Cubing.

Front

Solve for x: \(|4x−3| = 17\

Back

x = 5 and x = -3.5.

Front

What does it mean to isolate a 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 an extraneous solution?

Back

A solution that is derived from the process of solving an equation but does not satisfy the original equation.

Front

How do you check for extraneous solutions in radical equations?

Back

Substitute the solution back into the original equation to see if it holds true.

Front

What is the general form of a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

What is the principle behind solving absolute value equations?

Back

The expression inside the absolute value can equal either the positive or negative of the other side of the equation.