Solving Radical Equations and Inequalities

Front

What is a radical equation?

Back

An equation that contains 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, you can move all other terms to the opposite side of the equation.

Front

What is the first step in solving the equation √(x + 5) = 3?

Back

Square both sides to eliminate the radical: x + 5 = 9.

Front

What is the solution to the equation √(3x - 2) > 13?

Back

x > 57.

Front

How do you check for extraneous solutions in radical equations?

Back

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

Front

What does it mean if a radical inequality has no solution?

Back

It means there are no values of the variable that satisfy the inequality.

Front

Solve the equation (2x - 8)^(2/3) = 4.

Back

x = 8.

Front

What is the domain of the function f(x) = √(x - 3)?

Back

The domain is x ≥ 3.

Front

What is the range of the function f(x) = √(x)?

Back

The range is all non-negative real numbers: [0, +∞).

Front

What is the difference between a radical equation and a radical expression?

Back

A radical equation includes an equality (e.g., =), while a radical expression does not.