A2 Solving Square Root Equations

Front

What is a square root equation?

Back

A square root equation is an equation that involves a variable under a square root, typically in the form √x = a.

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.

Front

What is the first step in solving the equation √x = 5?

Back

Square both sides of the equation to eliminate the square root: x = 5².

Front

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

Back

x = 25.

Front

What does it mean if a square root equation has no solution?

Back

It means that there are no real numbers that satisfy the equation, often occurring when a negative number is under the square root.

Front

How do you check if your solution to a square root equation is correct?

Back

Substitute the solution back into the original equation to see if both sides are equal.

Front

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

Back

x = 0.

Front

What happens when you square both sides of an equation?

Back

Squaring both sides can introduce extraneous solutions, so it's important to check all potential 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 the equation √(x - 1) = 3.

Back

x = 10.