Solving Square Root Equations

Front

What is a square root equation?

Back

A square root equation is an equation that contains a variable within a square root. For example, √x = 5.

Front

How do you isolate the square root in an equation?

Back

To isolate the square root, you can move all other terms to the opposite side of the equation. For example, in the equation √x + 3 = 7, subtract 3 from both sides to get √x = 4.

Front

What is the first step in solving a square root equation?

Back

The first step is to isolate the square root on one side of the equation.

Front

What happens when you square both sides of an equation?

Back

Squaring both sides of an equation eliminates the square root, but it can introduce extraneous solutions.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation.

Front

Solve: √(x + 4) = 6. What is x?

Back

x = 32.

Front

Solve: √(2x - 1) = 3. What is x?

Back

x = 5.

Front

What is the domain of a square root function?

Back

The domain of a square root function is the set of all real numbers x such that the expression under the square root is non-negative.

Front

Solve: √(x) = -4. What is the solution?

Back

No solution, since the square root cannot be negative.

Front

How do you check if a solution is valid in a square root equation?

Back

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