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. It can be expressed in the form √x = a, where x is the variable and a is a constant.

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

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, leaving the square root alone on one side.

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

When you square both sides of an equation, you eliminate the square root, but you must check for extraneous solutions afterward.

Front

What is the solution to the equation √x = 6?

Back

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

Front

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

Back

It means that there are no values for the variable that satisfy the equation, often due to a negative value under the square root.

Front

How can you check if a solution is extraneous?

Back

You can check by substituting the solution back into the original equation to see if it holds true.

Front

What is the solution to the equation √(x + 4) = 8?

Back

The solution is x = 60, since squaring both sides gives x + 4 = 64.

Front

What is the significance of having two positive solutions in a square root equation?

Back

It indicates that the equation can be satisfied by two different positive values of the variable.