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 solve a radical equation?

Back

Isolate the radical on one side and then square both sides to eliminate the radical.

Front

What is the principal square root of a number?

Back

The non-negative square root of a number.

Front

What does it mean to square both sides of an equation?

Back

To multiply each side of the equation by itself, which can help eliminate radicals.

Front

What is the solution set of an equation?

Back

The set of all values that satisfy the equation.

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

Solve: √(x) = 9

Back

x = 81.

Front

Solve: √(4m^2) = 10

Back

m = 5 or m = -5.

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: 4√(x) = 20

Back

x = 25.