5.4: Solving Radical Equations

Front

What is a radical equation?

Back

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

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, perform inverse operations on both sides of the equation until the radical is alone on one side.

Front

What is the first step in solving a square root equation?

Back

Square both sides of the equation to eliminate the square root.

Front

What is an extraneous solution?

Back

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

Front

How do you check for extraneous solutions?

Back

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

Front

What is the cube root of a number?

Back

A value that, when multiplied by itself three times, gives the original number.

Front

How do you solve the equation √(x + 4) = 6?

Back

Square both sides: x + 4 = 36, then solve for x: x = 32.

Front

What is the solution to the equation x^3 = 27?

Back

x = 3, since 3^3 = 27.

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 where the expression under the radical is non-negative.

Front

How do you solve the inequality √(2x - 1) < 5?

Back

Square both sides: 2x - 1 < 25, then solve for x: x < 13.