Solving Radical Equations Practice

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 + 3) = 5?

Back

Square both sides to eliminate the radical: x + 3 = 25.

Front

What is the importance of checking your solutions in radical equations?

Back

Checking is crucial because squaring both sides can introduce extraneous solutions.

Front

Solve the equation √(x - 1) = 3. What is x?

Back

x = 10.

Front

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

Back

It means that there are no values for the variable that satisfy the equation.

Front

How do you solve the equation √(2x + 4) = 6?

Back

Square both sides: 2x + 4 = 36, then solve for x: x = 16.

Front

What is an extraneous solution?

Back

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

Front

Solve the equation √(x + 2) + 3 = 7. What is x?

Back

x = 7.

Front

What is the general form of a radical equation?

Back

A radical equation can be expressed as f(x) = √g(x), where g(x) is a polynomial.