Solving Radical Equations

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Front

How do you isolate a variable in a radical equation?

Back

To isolate a variable in a radical equation, you can square both sides of the equation to eliminate the radical, then solve for the variable.

Front

What is the first step in solving the equation √(x + 5) = 8?

Back

The first step is to square both sides of the equation to eliminate the square root, resulting in x + 5 = 64.

Front

What are extraneous solutions in radical equations?

Back

Extraneous solutions are solutions that emerge from the process of solving the equation but do not satisfy the original equation.

Front

How can you check if a solution is extraneous?

Back

To check if a solution is extraneous, substitute it back into the original equation to see if it holds true.

Front

What is the principle of squaring both sides of an equation?

Back

The principle states that if two expressions are equal, squaring both sides will maintain the equality, but it may introduce extraneous solutions.

Front

What is the solution to the equation √(x) = 5?

Back

The solution is x = 25, obtained by squaring both sides of the equation.

Front

How do you solve the equation 2√(x - 3) = 10?

Back

First, divide both sides by 2 to get √(x - 3) = 5, then square both sides to find x - 3 = 25, leading to x = 28.

Front

What is the domain of a radical function?

Back

The domain of a radical function is the set of all input values (x) for which the expression under the radical is non-negative.

Front

What is the importance of checking solutions in radical equations?

Back

Checking solutions is important to ensure that they are valid and do not violate the conditions of the original equation.