A2 1.5 Radical Equations

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 variable in a radical equation?

Back

Square both sides of the equation to eliminate the radical, then solve for the variable.

Front

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

Back

Square both sides to get x + 3 = 25.

Front

What is the importance of checking solutions in radical equations?

Back

To ensure that the solutions do not produce extraneous results when substituted back into the original equation.

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

Solve the radical equation: √(x - 1) = 3.

Back

x = 10.

Front

Solve the radical equation: √(2x + 4) = 6.

Back

x = 14.

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

How do you solve the equation √(x + 2) + 3 = 7?

Back

Isolate the radical: √(x + 2) = 4, then square both sides to find x = 14.

Front

What is the general form of a radical equation?

Back

An equation of the form f(x) = √g(x), where g(x) is a polynomial.