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 = 4.

Front

How do you solve a square root equation?

Back

To solve a square root equation, isolate the square root on one side of the equation and then square both sides to eliminate the square root.

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 a square root equation has no solution?

Back

A square root equation has no solution if the expression under the square root is negative, as square roots of negative numbers are not real.

Front

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

Back

The first step is to square both sides of the equation to eliminate the square root: x + 3 = 25.

Front

If you solve √(x) = 6, what is the solution?

Back

The solution is x = 36, since squaring both sides gives x = 6^2.

Front

What is the importance of checking solutions in square root equations?

Back

Checking solutions is important to ensure that they are valid and not extraneous solutions that do not satisfy the original equation.

Front

What is the solution to the equation √(x - 2) = 4?

Back

The solution is x = 18, since squaring both sides gives x - 2 = 16.

Front

How many solutions can a square root equation have?

Back

A square root equation can have zero, one, or two solutions, depending on the equation.

Front

What happens if you square both sides of an equation incorrectly?

Back

If you square both sides incorrectly, you may introduce extraneous solutions or lose valid solutions.