Solving Square Root Equations

Front

What is an extraneous solution?

Back

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

Front

What does it mean if an equation has no solution?

Back

An equation has no solution when there are no values that can satisfy the equation, often resulting from contradictions.

Front

How many solutions can a square root equation have?

Back

A square root equation can have two solutions, one solution, or no solution, depending on the equation.

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 is the importance of squaring both sides of an equation?

Back

Squaring both sides eliminates the square root, allowing for easier manipulation of the equation.

Front

What should you do after squaring both sides of a square root equation?

Back

After squaring both sides, solve the resulting equation and check for extraneous solutions.

Front

What is a radical equation?

Back

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

Front

Solve the equation: √(x) = 5. What is x?

Back

x = 25.

Front

Solve the equation: √(x + 3) = 4. What is x?

Back

x = 13.

Front

Solve the equation: √(x - 2) = -3. What is x?

Back

No solution, since a square root cannot be negative.